If gave lock-up or Mr. zsas the utility belt and used the batarangs, does pushing damage on all successfully hit targets count?

Pushing damage isn't damage from an attack.

but isn't incapacitate from opposing character considered an attack?

I mean sure it doesn't deal numeric damage in the conventional sense, but by reading how pushing damage is worded it says, damage dealt when a character receives a second action token. And if that second action token was given because of an opposing incap (ergo attack) ~ cause and effect?

Incap is an attack but it does not deal damage. Pushing damage, if any, is not from the attack, it's from having two tokens. While there is obvious cause and effect, that damage is not attack damage. That's why you can use Incap to beat down a Mystics figure without ever taking feedback.

alright. cool! thanks for clearing that up guys