Cantriped

Note: 
Avatar was a kids show... so people didn't usually suffer lethal injuries on screen. In a campaign simulating that trope, Killing Attacks might be prohibited.
In campaigns simply taking place in that world... Killing Attacks would be exceptionally common; especially amongst Earth Benders, but also Fire and Water. Martial weapons are extremely prevelant, though largely ineffective because the nature of the show prohibited them from being used effectively. The fact that Airbending techniques don't provide very many lethal maneuvers would also be so much more meaningful. I suggest finding out which campaign this is so you can tailor how you build your Bender accordingly.

I'd slap Gestures on everything; all the bending styles are super kinetic.

http://avatar.wikia.com/wiki/Earthbending has a pretty extensive list of abilities.

Actually, all of the Growth levels should be priced by starting with "the appropriate Size Template, and applying Costs Endurance (-½), Unified Power (-¼), and Side Effects (-½) to" the elements it contains (CC 69 and elsewhere), ignoring Complications (which are imposed by the side effect).
In other words, if you divide the total costs of the various size templates by 2.25 (and round) you get their Active Point cost as a Growth level... loosely speaking... this doesn't have to be a size template per say. You could use the principle to create all sorts of fairly priced custom Body-Affecting powers.

Variable Power Pool, or a Unified Power set. Maybe a Multipower if you know exactly what you want.
 
Let's look at what they do:
Make walls. Easy enough. Barrier covers that, you just have to figure out how thick and how strong, and if you want the limitations of being connected to the earth or no Earth Surfing. Whether it is pushing the ground away from you, or tunneling through the earth. Increasing Running speed with a limitation of on the Ground, and Tunneling are easy there too. Throw Rocks. You hurtle rocks around, if there is Ground. Blast with an easy limitation. Earthsensing. This is a fun one. Slap on Range, Discriminatory, 360 Degrees, Partial Penetration, and Targeting on the Touch Sense group. Limitation, only when touching the ground. That's a theme. Burried in Rock. Drawing people down into the stone and leaving them there. Entangle, only when they are touching the ground. I am the Mountain. Knockback Resist as they dig their feet in. Geokinesis. It's just Telekinesis, only in respect to earth stuff. Bothersome Sand and Dust. Flash or Darkness for Sight group. Your pick. Hmm... That's all that comes to mind right now. Then it's just which ones you want if it is a Multipower, or just grabbing these and anything applicable with a Variable Power Pool. Unified Power is almost expected.

When characters exposed to high or low Temperature Levels lose REC as discussed on 6E2 145. Treat the REC as being “permanently” lost until the character spends time in an area that’s at the Comfort Zone — every 20 minutes spent at the Comfort Zone allows him to regain one lost increment of REC.
 
For example, suppose that a character spends 40 minutes in Temperature Level -3 conditions. That means he’s lost -6 REC (and -6 END, though that doesn’t matter for purposes of this question). Fortunately, he finds shelter that maintains Comfort Zone temperatures. After 20 minutes in this shelter he regains 3 REC; after 40 minutes he regains the remaining -3 and is now at full REC.

I would go with the "Only in Secret ID" option rather than a Focus. 

Blooming criminy, aright. Reductio ad absurdum indeed...

Multishape: X points. Build is 5X points into Multishape. Repeat ad nauseum. You end up with X*5^N points for the character to blow on whatever the heck. Shoot, could have X*5^(N-C) for the points to have C^2 characters at that many points. Validity? Valid. Same option exists for Summoning, Duplicating, and adding to a normal person via Transform, and use of Follower, and use of other PC's.
 
I understand the ability for abuse that Transform enables, presuming one can use it on oneself. Understand, that ability for abuse exists already, simply taking a few more steps, or even in best case, for others, ad-nauseum. However, I would bet my eyeteeth that no GM with an interest in balance or character composition would allow this, or any number of options that allow such flagrant abuse. There is a reason these powers are marked with Stopsigns. It takes consideration on the player part to figure out what they are doing and GM to see if they are okay with it.
 
As it's not explicitly designated in the books that this is or is not an option, I'll leave it more up into whomever I mess with's GM to figure it out. Is it a slippery slope? Sure, so work with them to put up blooming guard rails. Or if they want, sheer off the top of the mountain. They are the GM, they can pick that option if they wish. 

Hero System Skills expands Analyze to other areas, including Analyze Motive, which if just made allows a PC to realise an influence skill is being use on them, and if made by a greater margin of success, which influence skill is being used on them, or whther they're being lied to.

Since you are using 5th, have you looked at Transfer (STUN into STUN) with Delayed Return/Fade and Only To Starting Values?
It won't kill your enemies, but it will let you play a kind of Drain-Tanker, in that your attack will simultaneously bring them closer to being knocked out and you further away. Once they are unconsious, just finish them off with a knife or something. The Transfered STUN will fade eventually, but you'll still be Recovering any lost STUN while it does, so with any luck by the time it fades you'll be be fully recovered anyway.

I hold an unpopular opinion on this subject, and say this at the risk of starting another long and fruitless debate... but: 
That only applies to Adjustment Powers that increase or decrease one of those elements (Aid/Boost, Absorption, and Drain/Suppress). Healing does neither; it very explicitly only restores lost points of an affected game element. In other words, it doesn't give you more BODY or STUN, it just restores points of them you've lost; as such it isn't included in the rule you quote... CC/FHC are far clearer on this point (although neither edition is as explicit as I'd like).
Unfortunately (for the credibility of my position), the 6e v1&2 rules for Healing have been muddied by Steve Long's official intrepretation of how Healing works, which contradicts the rules he actually wrote. In addition, once you include his most recent errata for those volumes (which he released suspiciously soon after a very long debate on the subject came up) the examples now support his position; but still contradict the relevent rules sections in every version of 6th edition. Using his official intrepretation, Healing is even worse than it's overpriced die and arbitrary per day maximums already made it appear. I would even go so far as to say his version of Healing is an unsalvagably inefficient point-trap on purpose. Which is an odd design conceit considering that the role of Healer is so unpopular that most systems have to bribe their players into playing one.

Actually one of the most overused lines in comic books is "how can something so big move so fast??" so the big=slow thing isn't necessarily a valid concept.  Plus, most of the big = slow thing came from movies using slow movements to emphasize their vast size, plus animation issues.  Elephants aren't any slower than weasels.

Don't forget you will need to buy ambidexterity to use those limbs appropriately (all extra limbs are considered off-limbs).
 
Martial arts will get you the "stick a finger in the eye" maneuver as well as others.
 
Clinging would also be useful as an easy way to grab onto things without needing both arms to use full strength.
 
Skills like sleight of hand for pick pocketing and lock picking comes to mind.  For lock picking, you might want discriminatory on touch to be able to use touch to identify things.
 
 
 

I agree, the balancing factor for healing is the limited uses.  Which works but to me feels more like a campaign limit than what truly belongs in a meta base rule set.  In other words: its probably a good idea, but shouldn't be hardwired into the power by default.  It ought to be suggested (or doubling, or some other limit) rather than required.  For some campaigns, it makes sense to have open unlimited healing, in others it does not.  A truly generic game set ought not force one campaign concept on all campaigns.

The full benefits of Telekinesis can almost be achieved using Strength, Stretching (in place of Range and Indirect), and Extra Limbs (to allow multiple grabs like TK)... If you don't look at the issue to closely.
 
But even in such cases TK has several unique advantages: For one thing, a TK Grab is a lot better than a STR Grab (and no amount of Stretching can make STR use the rules for TK Grabs instead), it is harder to block (because it is a Ranged Attack), and while TK Damage is more expensive, Martial Arts for TK aren't.
 
So in the end you are getting a lot more out of TK than you would from an STR "Punch" with Ranged (+1/2).
 
Plus there is the disadvantage that using Stretching STR still requires you and the enemy to be engaged in Hand-To-Hand Combat... even with Doesn't Cross Intervening Space, the basic effect of the power doesn't change: It grants you the ability for one part of your body to be up to Xm away from the rest of it (increased Reach is simply one of the more obvious benefits of that effect). Whatever part of your body you are Stretching "through a portal" (literally one of the 6e1 examples of Doesn't Cross Intervening Space) to grab them with is still within the target's reach, and thus can be attacked by them. The advantage of the Advantage in this case being that otherwise anybody could attack the outstretched limb... not just the target.

Punisher, like Wolfy and Timber Wolf, were at their most interesting when they were That Guy rather than Yet Another Bloodthirsty Killer.  When half of every team is packing huge guns and swords, it sort of loses its charm and unique nature.

No it isn't... but as a design principle it generally remains true. The stat you (and they) use to determine your (and their) CV isn't relevent to the type of damage the attack causes or against which defense it applies... BOECV is a corner-case where the same modifier can manipulate both, Based on CON (5eR 120) is another...
Regardless, a power like Blast or RKA won't change to STUN Only damage just because you apply a modifier that changes the CV it targets, it will only do so if that modifier also changes the defense against which it applies (such as to Mental Defense in some cases of BOECV).

Per RAW yes. 
 
You seem to be confusing aspects of Applied Versus Limited Defense with Based On EGO Combat Value (and for good reason).
 
The former (AVLD; 5eR 251) is used to create an RKA or Blast that applies against Mental or some other Defense (and must pay an additional fee to retain the ability to cause BODY Damage).
Meanwhile the latter (BOECV; 5eR 253) is used primarially to create powers that you Aim with your mind instead of your body (in other words, one that's attack roll is "based on" your "ego combat value"). However, BOECV does give the option to change the defense to Mental (making it act similarly to AVLD in that case), but that is an option, not a requirement. In later editions these modifiers were better differenciated to prevent confusion.
 
Psychokinesis only requires the BOECV modifier, and per the relevent sections of 5eR and the Ultimate Mentalist (which also includes the section of text I've quoted below from 5eR pg 231) defense is not noted as one of the changes made when BOECV is applied to Telekinesis.
 
So while the same BOECV Telekinesis could also be an entirely Mental Attack (which basically functions like a Mental Blast that can also be used to perform Grabs)... that isn't what 5eR is refering to as "Psychokinesis". Psychokinesis really is just bog standard Telekinesis with the following (and only the following) exceptions:
"It works on Line Of Sight and is not subject to the Range Modifier (unless used to throw an object at a target, in which case you should calculate the Range Modifier from the point where the character picks the object up). It is visible and can also be perceived with Mental Awareness. For purposes of using Psychokinesis, calculate the character’s OCV from his EGO, not his DEX, but the target’s DCV still derives from his DEX." (5eR 231)

Nice Ramble, but...  he is pretty much specifically talking about Psychokinesis example power as listed in the main books.
 
Which is Telekinesis, Based on ECV (ECV / OMCV vs. DCV)

Just out of curiosity, where is this second mouth?  Or do I even want to know?
 
For most campaigns I don't see this having serious impact on game play, so I would just call it Distinctive Features.  Yes, it might be slightly harder to gag or suffocate the person, but I think this falls within the realm of special effects.  Consider the various martial arts maneuvers that do NND; some are pressure point strikes that don't hurt those in rigid armor, some are choke holds that only affect those that breathe through their neck.  I don't have to pay any extra to define my armor as rigid, it is just conceptual and so a special effect.  Similarly, if I made a MODOK knockoff, he has no neck and can't be strangled, but I didn't pay points to move his face into his torso - it is just a Distinctive Feature.
 
If there is a major benefit for having a second mouth due to the nature of your campaign (strangle holds are very common to prevent spell casters from using magic for instance), then Extra Limb would be a reasonable way to go, but I think that is probably the exception rather than the rule.

Just a warning that Combat Healing is usually excessively expensive, and Healing generally seems to be intended to be used outside of combat. "Drain-Tanking" simply isn't a cost effective strategy in HERO compared to taking less damage (via defense powers) or doing more damage (via attack powers).

One of the advantages of the Hero system is the flexibility and variety.  A lot of games simulate this with special rules or powers given to individual items, but Hero has it codified and part of the system.  In other words, D&D might have a vorpal effect or an arrow that ignores damage resistance, but Hero has powers that tell exactly how and why that works, and you can buy it with a spell or character ability rather than handwaving it.
 
Killing damage is one of those variants in the rules; it allows certain classes of weapons to bypass a certain kind of defenses, and the system allows for distinction between say a club and a knife.  Further variants like armor piercing, increased stun multiple, and so on allow greater distinction between weapons.  That way instead of weapons just being x damage, x weight they are unique and each one has its own special characteristics which can be taken advantage of or not as useful in a given situation.  Kind of like real life weapons.
 
This adds a layer of complexity to the game, but a fairly minor one -- and as I noted above, the complexity is back doored into other "more simple" games through an endless and largely arbitrary series of exceptions.

Transform is an umbrella for Attacks that impose unusual conditions (like having an extra mouth)... not for possessing an unusual feature yourself. For that we have Distinctive Features, Striking Appearance, or Extra Limbs (depending upon how the feature affects the character)

That results in all the associated problems of using a Transform to do "that thing I just can't figure out any other way to do." 

I should clarify that when I said PDF of the rulesbook I meant a PDF of CC/FHC (which are very nicely organized and bookmarked)... It takes me forever to find anything in 6e V1&2 so I rarely use them.
For in-session reference I vastly prefer to have hard-copies of the rules handy. During play I only use PDFs to reference seldom-used NPCs.

Yes, an Attack Power with Requires A Roll must be rolled first to activate, then to hit (and then for effect of course).