Re: transport familiarity requirements
Well, you can do anything your GM will let you do, but I’d recommend that if you’re using the full rules, you stick with ’em. Trying to mix the slimmed-down SK rules with regular 5E rules might result in some characters getting an unfair benefit.
Just to make sure everyone’s on the same page, to use TF: Carts & Carriages, a character also needs a TF for the appropriate riding animal — not Riding, which is a separate Skill.
If a character chooses Carts & Carriages as his free TF for Combat Driving, he still needs a TF of the appropriate riding animal to use it.
Any equipment a character buys with Character Points, he automatically knows how to use without the need for a Skill — but as covered in the Rules FAQ, TUV, and eventually 5ER, that extends only to that one piece of equipment. Paying points for a cart (a Vehicle) only allows the character to drive that one cart without a Skill; it does not grant him TF: Carts & Carriages.