Red Shift attacks and uses his remove from game ability. I have 2 scenarios I have questions about

1) If he attacks a character who lost his cosmic counter, does the character get it back when he comes into play?

2) If he attacks a character who has a power with the "use this only once per turn" clause, can he use the power once before Red Shift attacks and then again when they come back into play?

edit because I can't count to 2

1. Characters that have the cosmic keyword come into play with a cosmic counter on, so yes.

2. If a card changes zones, it is a different character, so yes (90ish percent sure on this one; certain of the other)

Yes. Unless the card says othewise, Like Alfred Pennyworth they alway come into play ready, so you can exhaust a character then when it gets red shifted, it comes back ready. As for cosmic, as long as it's not cosmic surge, yes.

If they have cosmic surge and have a cosmic counter, would they lose it when he comes back into play?

Yes. And because they come into play off his triggered effect after the start of the recovery phase, they don't get the one they'd normally get had they stayed around unstunned.

So does Jean Grey, pheonix rising lose her counters? And if she doesn't does she get more counters coming back into play? I ask because of bodyslide.

When cards change zones, they're no longer the same cards. Technically, a card isn't returning to play, or coming back to play---a new card is entering play. And counters are always lost when a card changes zones, so the one in the RFG zone never has a Cosmic counter, never has a +1/+1 counter, etc.

And if a card is brought into play by a modifier like Bodyslide's or Red Shift's, you treat it like any other enters-play event.

so with that said..redshift comes back into play with his cosmic counter right?

Yup. He's Cosmic, and not Surge, so he has it on him as he enters play.