Say an opponent has willpower/indomitable and attacks me, giving himself his second action token. Now during my turn I outwit his willpower/indomitable, after all actions resolve and at the end of my turn does he then take a click of pushing damage for having two action tokens with no willpower or does he only take pushing damage during his turn?

Pushing damage usually happens AS an action resolves on an action where a character received a second action token.

It can happen on any players turn, and it can only happen as an action is resolving. There isn't a way (that I'm aware of) to cause a character to take pushing after an action has resolved.

You could outwit his willpower on your turn, then maybe follow up with an incapacitate attack or something else that will place a token on the character, but that's about it.

Just outwitting willpower on a character that already has two tokens isn't going to result in push.

Making sure that second token gets applied to a character with only one token, though...

What happens if I have my characters willpower outwitted and I push to attack the character that outwitted my willpower and knock them off of outwit. Would my character gain willpower back before pushing damage is applied or would I still take my pushing damage?

The Willpower will return as soon as your target loses OW from taking damage.after that, as your action ends, pushing damage is applied. You got your Willpower back already, so that push damage would be ignored.

yeah if the outwit that countered your willpower is gone than your will power is back, so as long as outwit is gone before your action ends than your willpower will be back and you can choose whether or not to take the push.