I have a question cause me and my friends are having a 126 man, 1 vs 1 knockout tournament.

Thanos skill dissension in your ranks says opposing characters can not use team abilities. If a power cosmic character is adjacent with hypersonic speed and one token on him. Can he use hypersonic speed to get away from being adjacent without putting a token on him. Argument being is that power cosmic will kick in after he breaks away thus not resulting in pushing damage.

Sorry should say put second token on but without taking pushing damage.

After actions resolve he is not adjacent so he can use his team ability.

No, "opposing characters cannot use team abilities" means exactly that NO OPPOSING CHARACTERS ON THE MAP can use Team Abilities. If the character takes an action and he already has one action token the character will take pushing damage no matter where he ends his turn on the map.

I think DarthUr is correct.

Yeah, or you could read the power he's asking about.

So if he successfully breaks away he will not take pushing damage?

Yes.
Remember that you do not place an action token until after your action resolves. And that is when you check to see if you take the pushing damage.

Hey, that's on him for not quoting the power in it's entirety and you're right the Character would regain the use of the Team Ability once the character is no longer adjacent to Thanos

This is true.

This is also true.

Yeah sorry about that.