If you push a character on the last action of your turn and he gains a free power like outwit or perplex, can you use that power even though all of your actions have been used for that turn before you remove any action markers from any of your unused characters? Or, does your turn immediately end and you can't use these free powers?

yes you can use any free actions at any time during your turn

But that's not the question...I know that you can use those free actions at anytime during your turn. The question is does your turn end with your last action so you can't use those powers?

No it does not BECAUSE of the possibility of free actions. Your turn ends when you tell your opponent your turn is over.

Ahh. Thank you very much.

Don´t forget a character can only do ONE free action. I mean, (for example veteran Captain america) if you had used your character´s leadership at the beginning of the turn, and after pushing it later, it gained outwit, you wouldn´t be allowed to use its outwit.

Yes, you are able to use powers that appear, even at the end of your actions. Your turn is still going, so it's perfectly within the rules. Like mentioned before, your turn doesn't end until you declare it is over. Therefore, you are free to outwit anything on your opponent. Perplex would be useless in this case, though.

This is incorrect, you can do as many free actions in a turn as the powers allow you. For example V Ult Beast can Perplex his damage, push to attack, then use his Outwit afterwards.

And yes, V Ult Captain America can use his Leadership and push to use Outwit in the same turn.

This is wrong and here is why: