1. does catman protect from total anarchy? I think so but I'm not sure when anarchy triggers so i want to make sure.

2. ragdoll--lets say she gets stunned and I discard a card for her effect. Then in the same comabt phase something happens and I nned to recover her(to avoid a finishing move or something) then she gets stunned again. Do I have to discard again to ensure her recovery at the start of the recovery phase?

1. Catman will protect from your opponent's Total Anarchy, not your own. And the characters need to be stunned, so make sure not to recover them before Total Anarchy's resolved.

2. By discarding, you've set up a delayed trigger for the start of the recovery phase. The trigger still exists, no matter what else happens to Ragdoll in the turn; even if he's removed from the game, that delayed trigger will still exist and try to recover him.