Peter The Hunter
Killed My Greatest Enemies: when Peter the Hunter KO's an opposing character of 50 or more points, after actions resolve heal him to click #1 and place a Trophy token on this card. When Peter the Hunter would be KO'd, you may instead remove a Trophy token and turn him to his last non-KO click

I have two questions about this character and this trait, first is if peter the hunter pushes to kill some one does he heal first or take pushing damage or is there an order?
also can this trait be countered with outwit. i think this character is awesome but with out it is a bit confusing about the order of this power with pushing damage

To answer your first question, his trait and pushing damage occur "after actions resolve" so as the active player, you get to decide in what order to resolve this. EDIT: As pointed out by bluerat, pushing damage occurs "as actions resolve" so in your scenario, Peter the Hunter will take the pushing damage before anything else happens, this would trigger the "Killed my Greatest Enemies" second clause using a trophy token (if you have one) and then the first clause would trigger healing him to top click.

The second answer is, no. Traits cannot be countered by Outwit. There is currently no way to "counter" or turn off traits. Due to the can of worms that would open, there will likely never be a way to do so (but I wouldn't bet on that). However, when the new rules roll out, powers granted by traits will be outwit-able (provided the trait or character isn't protected from outwit).

I am fairly sure pushing damage happens after the action is completed but before any "after actions resolve"-effect takes place. It's "as actions resolve" rather than "after actions resolve".

So in this case pushing damage would occur first.

I just checked my rulebook and you are correct. How did I never notice this?

I checked older rulebooks and pushing damage was once "after actions resolve" but not any more.

Thank you for the correction, bluerat!

I had to look it up as well and check the difference between "as action resolve" and "after actions resolve" it's not something I think you would know unless you've come across it before.