Gnome BODY (important!)

Fair enough.
 
Then the main concern is what zslane brings up:  Are they indeed gradually learning the game system?  If so, then I guess all is well.
 
Maybe it's my own vestigial remnant of the D&D "box" that I still want my character to get better, more skilled, more powerful, over time.  I want those experience points!  And I want to spend them sooner or later, to gradually improve my abilities, or maybe to buy new ones.
 
OTOH, I think that's also part of my desire to play a hero - something very much not in the D&D box.  I want to be one of the good guys - not just to say it and be recognized for it, but to actually do as much good and heroic work in the fictitious world I'm playing in.  And the more powerful I am, the more good I can do.  I want to rid the world of evil and create my own line of hair care potions.  I want to eventually defeat Kal-Turak/Doctor Destroyer/etc.  And I can't do that as a starting-level character.  I don't just want to be, as some here have put it, a "murder hobo".

I forget who first said that Hero (as opposed to a game powered by Hero) has its complexity front-loaded into character creation, so it is the first thing the player sees.  They can build an ineffective fighter or wizard in D&D, but the system makes it harder to do so, and provides easy, generic starting character "templates".  RESULT:  Hero appears more complex.

You will find opponents with ranged attacks are pretty common in Champions games.  Again, I am assuming you will be playing in a typical Champions game.
 
 
Let's break it down.  If she Dodges, she gets +3 DCV, and that is her attack action for the phase.  She has DCV 9.  If she uses one of her electrical attacks, and assigns her three skill levels to DCV, she has a DCV of 9 and gets to attack at OCV 6, possibly taking down one of the SWAT team.
 
Which do you think is more likely to be a successful tactic:
 
(a)  having 9 DCV and getting an attack; or
(b)  having a 9 DCV and getting no attack?
 
A 6 OCV is not overly high for "agent level" mook opponents in a Hero game.  With a DCV of 9, if all they do is stand still and fire away, they hit on an 8-.  That's about a 25% chance.  You will be taking a hit (possibly more than one) every phase.  You cannot weather those hits.  Your claim that you will "mop the floor" with those SWAT agents is, therefore, exceedingly optimistic.
 
 
I don't recall you explaining why Joules would be trying to mop the floor with a SWAT team either.  OK, the SWAT team works for a foreign government, and they are guarding your imprisoned teammates who are held in ColdSleep.  You are their only hope before the foreign government drives them away to dissect them and figure out how their powers work.  Their orders are "guard the prisoners", not "chase down anyone who comes across your path", so you can certainly fly away and avoid battling them, if you wish.  However, that is a win for them, not a loss, because they do not care whether you are captured or free, or dead or alive, as long as they fulfill their assignment of delivering the prisoners for dissection.
 
 
Because we are testing your theory that Joules can mop the floor with a squad of SWAT agents.  If we assume a bunch of options to find cover, then I think we also have to assume the SWAT team is also capable of making effective use of that cover.  In my "guard the prisoners" scenario, it seems likely they would already be entrenched, but we did not place Joules at that added disadvantage.
 
 
Gnome provided his source.  The Competent Normal on p 440 of Hero 6e V1 has CVs of 5 and SPD 3, so I think that may be transplanted into whatever source you are using.  He also has a weapon familiarity, a bunch of user-designed skills and 9 points of user-designed skills and talents.  That's more than enough to get the skills that Gnome has incorporated.  +1 OCV is 5 points and 2 +1 OCV levels with pistols is another 4, so there's that 8 OCV.  It is a 100 point build, with no equipment.  The handgun, SWAT armor and truncheon are not likely worth 50 points, all in.  Overall, I would say that these SWAT agents are Competent Normals with their discretionary points allocated to their profession. 
 
They are not likely any more powerful than agents who would be used in a typical Champions game, outnumbering the heroes 5 or 10 to 1 if they had no non-agent support.
 
 
I will give her the benefit of the doubt that she figures out she can get the same 9 DCV if she fires an electric blast as if she Dodges.  So, Phase 12, she shoots first, OCV 6 vs DCV 5.  Needing 12- to hit is almost 75%, so we'll assume she hits and takes out one member of the well-spaced SWAT team.
 
Since it is Phase 12, all 6 get to shoot back.   They need 10- which is a50% chance, so three should hit.  Cribbing Gnome's first three hits, Joules is now at 15 STUN, 4 BOD.  She recovers 10 STUN.
 
Phase 3, she can fire first.  Let's assume two cops are close enough that she can Spread.  She hits both with her 12- (3 for 3 - OK for 74%) and both are KOd.
 
The remaining four fan out and fire, still on a 10-, so 2 hit (50%).  Cribbing Gnomes' net two rolls, Joules is now at -7 BOD and -3 STUN.  She gets a recovery in Phase 5, so now she has 7 STUN and 7 END.  Joules moves first on Phase 8, stands up and uses all but 1 of her remaining END to blast.  However, she has a 75% chance to hit, and this is her fourth shot, so she misses.  The four cops can either shoot her (two hits will likely kill her since she is already at -7 BOD, and she will for sure be KOd past PS 12).
 
GAME OVER
 
 
First off, 12d6 is pretty average offense in a typical Champions game.  I am not sure whether you are playing a typical Champions game.  Again typically, an equal number of villains to heroes are encountered, many villains have ranged attacks and/or are pretty mobile, so you may well pop up and attack, however one of the villains is likely to target you afterwards.
 
Champions does not play like D&D where the fighters block the hallway and no one attacks the spellcasters.  It is not a dungeon crawl where you will virtually always be able to decide who goes in first and who might hold back, unnoticed until they act. 
 
 
So which characters have you seen that have DCV 6 and less than 10 defenses, with only 3 resistant?  Typical justifications for enhanced defenses would be a force field or a costume with some rDEF.
 
But hey, maybe your game is not Standard Champions Supers and this character will be fine.  Have you asked other players in the game to look over your character?  Have you asked your GM?  Do the Brick and Battlesuit have similar CVs and markedly lower damage?  Would Joules easily hit them?  Would a 12d6 Blast or two take them out?
 
Massey, Gnome and I approach this from our experience, in typical games we have played in.  The game you are building for could be completely different.  But if it is a typical Champions game, I don't think your build will be very successful.
 
Clearly, you disagree.  From your comments, Gnome and I are full of ****, and the character's defenses are fine.  So run the character and let us know how it goes.

I'm of the opinion that giving new players (any players really, but mainly new players) access to information out-of-character that they don't have in-character is a Bad Idea.  They're learning to pretend to be their characters, don't make them multitask by also pretending to not know things.  The human brain is not good at having-but-not-using information because it's very good at having-and-using information. 
 
That said, I feel that the sharing-of-secrets is a great way to bring a party together.  I'd personally suggest running adventures early on in which revealing parts of the background will make things much easier, then follow that up with reveal-adventures wherein the secrets come to light. 

Oh no, they really want to play.  They love playing.  I can assure you of it, I've seen all the do-nothing-outside-game-time players get together and cheerfully organize a session before.  Setting, system, characters, the works.  But only during game time.  They just really don't want to spend non-play time on play-things.  They want to play TTRPGs, but only in one or two 4-8 hour chunks a week and not at all outside that. 

Oh no, they really want to play.  They love playing.  I can assure you of it, I've seen all the do-nothing-outside-game-time players get together and cheerfully organize a session before.  Setting, system, characters, the works.  But only during game time.  They just really don't want to spend non-play time on play-things.  They want to play TTRPGs, but only in one or two 4-8 hour chunks a week and not at all outside that. 

I sucked majorly, but that's what the GM wanted to run and at the time there were no other GMs. But even that didn't stop most of us from quitting his game and deciding it was better not to play at all then play in his games.

I find this sad.  People have become so used to being "hemmed in", that they've forgotten how to be free.  They've been "institutionalized" like Brooks in Shawshank Redemption.  Like the Israelites leaving Egypt, they have to wander in the desert for forty years to shake off the slave mentality.
 
People have been playing role-playing games probably for almost as long as there have been people.  They just didn't have formalized rules until the late 1970's.  Formalized rules are a good thing, so you can have fairness, and don't have to argue about everything ("I got you!"  "No, you missed!").  Unfortunately, formalized rules can also take away the freedom and creativity that you can use when you don't have formalized rules.  So the best situation is a system of formalized rules that preserve the full flexibility of being able to build and do whatever your creativity can come up with.
 
In the case of new role-players who have no interest in reading the rules, and have no desires and goals regarding spending their XP - or how they want their characters to grow - it sounds to me like people who really don't want to play.  Or maybe they just haven't grasped the basic concept of role-playing games.

Heed the caution signs in the rules is a great start.  Don't try to build stuff like the Constant INT Drain.  Sure you *can* but that doesn't mean you *should*.  Look at ACTIVE points.  That 40 STR TK w/16m radius is 105 active points, at least in 6E.  That's equivalent to a 21 DC attack.  
 
Played a fair bit of 3E.  There was one GM who liked taking what you did and designing against it.  I remember the end of one session where a player we knew, but his first session in this game...built a high-speed, high-Dex flyer.  So that GM unleashed a 5 shot, based on ECV, autofire killing attack.  Dead PC.  He (I still think wilfully) ignored additional cost aspects...like, Autofire Based on ECV 5 shots isn't +1/2, it's + 1 1/2.  He almost certainly misused Charges.  He made it a killing attack when there was no need to do so...for reasons too long to get into, this was supposed to be D&D "magic missiles."  
 
An interesting approach, IMO, is to play, literally, a No Limitations game.  Add 20% to each character's starting points maybe...but no limitations for which you get points back.  You can build Power Armor guy...but the armor's not a Focus.  I've got a build for a tough martial artist, with Extra Limbs and Stretching...only with the extra limbs.  He's got +STR, only with the extra limb, IIRC.  Fine, those are the concept, so the limitations are real...but for this concept they're SFX, not Limitations.

Oh, and Supergirl's heat vision on the TV show.

Ablative Armor, Captain America's Shield,  or Wonder Woman's Bracelets.

I'm of the opinion that giving new players (any players really, but mainly new players) access to information out-of-character that they don't have in-character is a Bad Idea.  They're learning to pretend to be their characters, don't make them multitask by also pretending to not know things.  The human brain is not good at having-but-not-using information because it's very good at having-and-using information. 
 
That said, I feel that the sharing-of-secrets is a great way to bring a party together.  I'd personally suggest running adventures early on in which revealing parts of the background will make things much easier, then follow that up with reveal-adventures wherein the secrets come to light. 

I'm of the opinion that giving new players (any players really, but mainly new players) access to information out-of-character that they don't have in-character is a Bad Idea.  They're learning to pretend to be their characters, don't make them multitask by also pretending to not know things.  The human brain is not good at having-but-not-using information because it's very good at having-and-using information. 
 
That said, I feel that the sharing-of-secrets is a great way to bring a party together.  I'd personally suggest running adventures early on in which revealing parts of the background will make things much easier, then follow that up with reveal-adventures wherein the secrets come to light. 

I think you're right. My point is that, as "Realism" is already being taken further in TTRPG than in fiction, why push more into Realism than the game already is structured for. It would be very tedious to write up complications for riding animals that make you roleplay out realistic horse handling (even if you didn't have to write up the complications and instead decided to just roleplay it out), when in almost no genres are those details relevant. My point is, it is neither relevant to the genre nor easily supported by the system. So it's not a matter of "TTRPGs just tend to be more realistic than fiction," when such compunctions don't necessarily originate from the system, and also aren't represented by source material.

Personally, I would do it like this:
 
20 Regeneration (20 BODY per Week), Can Heal Limbs, Resurrection (65 Active Points); No Conscious Control (-2), 1 Recoverable Charge (Recovers Under Limited Circumstances; -1/4)
 
5 Teleportation 3m, Safe Blind Teleport (+1/4), Reduced Endurance (0 END; +1/2), MegaScale (1m = 1 km; +1) (8 Active Points); Linked (Regeneration; -1/2)
 
The regen is no conscious control because the character doesn't know if he's gotten enough credit to respawn or how much time it takes in bureaucracy.  The 1 recoverable charge with limited recovery is based on if they do enough good deads in this new life to earn them another respawn.  The teleport is enough to put them somewhere safe with about 1 mile of the body/death site.

Loving the rolls as randomizer on the "when!". However, that implies a need for carting out all the possibilities, time-wise, and tying them to the results:
 
Make it by ten (combined between beuticratics and contacts)?  You're only here two days.  Make it by four?   Six weeks.  That sort of thing. 

Characters and NPC's use INT Rolls to make memory checks. So first I'd ask the GM to make a chart with the modifiers of things that would effect that roll. For example, a one on one conversation gives +3 to check, no communication and in a crowd gives -3 to check, making a "scene" gives +2, every two steps down the time chart is a -1, etc... And NPC's will remember major and minor events they are part of (that they went to that party) but they might forget details about who was there, who they saw, etc... In real life this can happen a lot, especially under stressful events, witness to crimes often have very different descriptions of the perpetrator of the crime, even if it happened just a few minutes ago. 
 
After the chart is made and base rules agreed on, then a build like this might work:
 
 Forgettable:  Change Environment (-5 to INT Roll, Long-Lasting Permanent), Area Of Effect (10m Radius; +3/4) (54 Active Points); Only vs A NPC's check to remember details of the Player (-2), No Range (-1/2)) RC:15
 
Players has to activate the ability, for 5 END, but after that the effect is permanent. Everyone within 10m of him for the duration he is using the ability, will after that and forever have a -5 to INT rolls to remember details of the character. Again, NPC's will remember events happened. If the Player stands on a table and shoots a someone the NPC will obviously remember that event forever, but this ability means he/she will have a hard time remembering any important details of the character or identifying him later. If the Player has a distinctive feature disadvantage, the NPC will always remember that feature, but might not remember any other specific details. 
 
Note: this is built saying an NPC's check, meaning it only effects sentient characters, and does not work against cameras and the like. 

I was planning it to be a foregone conclusion, just for the sake of not dealing with morality arguments at the table.  Or worse yet, after-the-fact morality arguments at the table. 

Because, with 3 Resistant Defenses, she is pretty easy to kill with a gun.  What tactics do you think she would logically use in this scenario?
 
 
Because that would provide the same +3 DCV she received from assigning her skill levels to DCV, and she cannot attack while dodging, so she cannot use her Electric Attack skill levels and Dodge at the same time.
 
 
I assume because she was so confident she could mop the floor with a squad of SWAT agents.  If she decided to flee, she might escape.  Will fleeing the scene be her usual approach to combat?
 
 
A valid question - how far apart are the cops standing?  How many dice do you want to sacrifice? 8d6 vs 5 or 10 defenses will at least STUN an average member of this SWAT team.  Actually, spreading for a lot of area would pretty much duplicate that Champs Electrique, further highlighting its lack of utility.
 
 
As indicated above, they are "Experienced/Tough Cops" as defined in a Hero product.  I believe they have OCV 5 (so not Legendary) and +1 OCV with their guns, judging by the description.  Few of those hits were just barely, or only by one, so dropping their OCV by 1 or 2 might drag it out a bit more, but will not likely change the outcome.
 
 

Didn't your die rolls also not count unless they went uphill and ended in snow? 

This is precisely how I do it with a villain called "Fade."  He and UltraViolent both received their powers at the same time during the same "radiation accident." Both of them are invisible.  Fade's "invisible," however, is that people just flat don't remember him.  He's there.  They'll bump into him, talk to him, interact with him-- the minute they're not looking directly at him, they totally forget he exists:  they think that _maybe_ they saw / talked to someone, but couldn't begin to describe him.  They couldn't pick him out of a lineup of two.
 
Been using him off-and-on as an assassin and / or bodyguard type since....   I don't remember.  Before 1990, I remember that, because we had a New Year's game going into 90 where they finally managed to catch him.  They hung a sign on his neck so they'd remember who he was.  
 
Turns out that his powers make him extremely hard to keep imprisoned, though.  All he needs is access to an open door without his shackles on.
 
 
You don't really need the Telepathy:
 
If you were "regular invisible," you'd have no features to remember or to describe.  You are just using that part of the Invisible power structure.  You can call the fact that you are actually looking right at a guy that you don't know the "fringe effect" if it makes you feel better.   Honestly, it's one of the most elegant builds I've ever done, and have been repeatedly surprised at how disturbingly effective it can be.  
 
 

So the way I was seeing this, this guy, who's moniker is Da Vinci (because he really likes art) basically slips from the mind of other people. I bought him a complete invisibility to everything, no fringe, always on, inherent.
 
Unless the guy concentrates to become visible, he could just as well not be there at all, there's basically no way to crack into his cloak. However, it doesn't work on machines and very simple minds : the simpler the mind, the lesser the effect. A fully-functional human will simply never register him besides a weird impression when reminding the events, a baby or a comatose human might perceive a shadow or a silhouette, a dog will feel his presence and might see a blurry picture etc etc
 
This also means, while people might see his face when he concentrates to speak to them, it'll just vanish and they'll only remember bribes of the image (like how people imagine things or remember dreams, just patchwork of blurry elements, not even shapes or colors, memories of memories). They will remember what he said, the gestures he made, the way he was dressed, etc. 
 
At first I was thinking something along the lines of a distinctive feature "No Face", disadvantage... But now that I'm thinking about it, it really sounds more like just flavor? 

And that nicely sums up my "meta-game" problem with NCM / RCM.  The best solution I've found is that when it is appropriate, it applies to _all_ player characters, and is a zero-point "way the world works" kind of thing.  Though to be honest, I don't use it much.  Too much headache owing to repeated arguments from players that are akin to what Ninja Bear posted:
 
(Not picking on you, N-B.  Not even remotely.  It's just such a perfect example of why I don't usually use it)
 
 
Let's take the idea that a player wants to make some kind of "small race" character-- halfling or some such, and make him an acrobat or a thief or something along those lines.  He decides he wants NCM / RCM at 25 pts worth, but wants to buy his DEX up a bit because of his agility and sleight of hand skills.  So he decides to spend 6 points to bump his DEX up from his Reduced Maximum of10 to a 13, then spends ten more points to move it up to a DEX 15.
 
The player is _fine_ with the other reduced Characteristics; they do not impeded his plans for the character or the development he plans for that character in any way.  it will never come up in game play, as it's not a recurring problem or a Hunted or a reputation or anything like that: if he has an STR 8 with a racial RCM cap of 15, that's not a handicap.  It's no more a handicap that having a superhero with a 15d6 Blast trying to take a Limitation that it costs double to increase that Blast beyond 25d6.  It's not something the player wants to do anyway.
 
But with our halfling acrobat, he gets 250 points because he's decided he doesn't want high characteristics save Dex.  He spent sixteen of those twenty-five to raise his DEX, and now has nine character points "extra" to either raise his characteristics or buy his acrobatics abilities with.    He's not only "not really limited" in this case, he's coming out ahead: he got effectively-free points to dump into his characteristics.
 
 
There's a meta-game problem here, at least for me.   If you don't see it, well-- that's fine.  Seriously.  I discovered this years ago: there are some things that have been problematic for me in the past that a large majority of the community just doesn't see as a problem; there are things that the community espouses to be a problem that have just never come up in my games.  It happens.
 
 
But for my money, I'd rather make NCM (on the rare occasion that I use it) be a zero-point everyman complication, and just build "racial templates" for each race-- well, let's face it:  Package deals-- to avoid all the problems that RCM causes me.
 
Different takes, I suppose. 

My POV: How do the characteristic caps hinder the character compared to a character with the same statline but no caps?  If the answer is "They don't", they're not worth anything. 

So, how many GMs in a 5e or 4e game would allow my Archer Elf*?  He spends 90 points on a 30 DEX.  10 OCV and DCV, and 4 SPD, out of the gate.  He has 60 points left for weapon familiarities, some other stats skills, etc. and maybe an Archery Trick or two.  He can boost a lot of those with xp later, of course.
 
Or Halfling.  Or, for Duke, anthropomorphic tree frog.
 
Actually, forget it - he'll have a 20 DEX naturally, +10 DEX, No Figured (-1/2), not if he ceases to venerate the Great God of Elven Archers/Elvish Slingers/ Tree Frogs (-0 limitation).  Since limited characteristics don't attract NCM, he only pays 60.  He can invest 10 into +1 SPD to get that 4 SPD back.  That leaves 20 more to spend as he sees fit. Maybe another +2 SPD, not if he ceases to venerate the Great God of Elven Archers (-0 limitation)?
 
Nope, no problems with the NCM rules...