i Was wondering if you give some one an action token does that mean that an action was given to them? For Example, can a charqacter who has been carried be given an action token for any reason?

You can't just give an action token to a character because you want to. You have to give them some kind of non-free action or through some other game effect that will give them a token.

You can give a character a move action and not move any squares. If your looking for other ways to get tokens on characters with game effects other people might be able to help out, but it's not really a rules question.

You can give a token to a character to do nothing but only if it could legally be given a non free action at that time. (Basically the move action described above.) In your example the token would have to be given to the character before it was carried not after.

There are several effects that grant action tokens without requiring actions on the part of the character. Incapacitate, obviously, though you can't depend on your opponent to do it to you when you want. Theme team PC is not an action but gives a token. Since it isn't an action, you can have a character get a token for using it even after that character has been carried.