For characters that have restrictive uses of things, like Ant-Man 026 from CW's SP:

IRREDEEMABLE LIAR: Ant-Man can use Outwit, but only to counter an opposing character's Outwit or Perplex, or a special power that specificially allows the use of Outwit or Perplex.

Would he be allowed to use Thwart?

Prerequisites: Mastermind or Outwit
Choose a character.

Give the character a power action. Place a thwart token on a target feat card assigned to a character that is 10 or fewer squares from the character and to which the character has a clear line of fire. The target feat is ignored until a character to which it is assigned is given a power action specifically to remove the thwart token.

USING FEATS
To use a feat, the character must possess or be able to use the game effects, powers, and abilities specified by the prerequisites of the feat.

and

USE AND POSSESS
A character possesses a power or ability if that power is printed on their dial in the form of a white or colored square, or if an icon granting that ability is printed on their base. A character may also possess a power or ability if a special power or trait ability states that they “have” or “possess” that power or ability.



A character uses a power if a special power or an ability states that they “can use” or “uses” that power.
A power or combat ability that is possessed by a character can be countered. A power or ability that is only “used” by a character cannot be countered, though often the power or ability granting use of that power can be countered instead.

i would say yes

This one works fine so far as i can see- He's being given an action for a special kind of action, not a special use of Outwit. Just because he cannot use outwit normally, it doesn't interfere with the way Thwart works.

(unlike all those -2 perplexers during a brilliant tactician making it useless ^^)

However, there are other types of special powers with other limitations on them. For example:

Aquatic Rejuvenation: If Namor occupies water terrain, he can use Regeneration.

Namor can only use Regeneration if he is in water. If he is in water, he could then use Automatic Regeneration. If he wasn't in water, he couldn't use the feat.

AUTOMATIC REGENERATION
Cost: 12
Prerequisite: Regeneration
Choose a character. Once, at the beginning of your turn, this character uses Regeneration as a free action.


Take home message: just because you see the name of a standard power in a special power or trait doesn't automatically mean that character can use that standard power as a feat prerequisite all the time. Double-check for any kind of activating conditions, first, before you go slapping a bunch of extra points on that character that it may or may not be able to use effectively.

While we're on the subject of Ant-Man, what happens when he takes the Pym Particles Feat?

Pym Particles
Prerequisites: {starburst}, Avengers TA
Choose a character.

Once per game, choose one - the character has the {giant} damage symbol; or the character modifies its defense value by +1 against ranged combat attacks. The chosen effects last until the end of the game.

Since he possesses both Tiny and Giant, can he be carried, can he carry?

He doesn't have both. When a character is given a new combat symbol, it replaces the old symbol unless you are specifically told otherwise. This does not say otherwise. Ant-Man ceases to be , becomes , and can do everything the normally does.

Alrighty, cool stuff! Thanks.

So a 20 defense, stealthed, 4 range giant... or 22 defense against ranged attacks... I really want that guy now...