Her normal state is be non-powered, but she can absorb and (usually does so) the powers of others. Whole or just fractions.
She lost Ms. Marvels powers a long time ago, but she did reabsorb them along with her EP during the last fight of the two. Temporary, I am afraid.
Rogue couldn't be an Avenger so long as she has an outstanding criminal record. As far as I know, she's never been pardoned for her actions as a terrorist in the Brotherhood of Evil Mutants. She did considerable damage to Ryker's Island, and battled the X-Men at the Pentagon. And she didn't have the benefit of having been forced into terrorism like Wanda and Pietro. I don't see how she could be credibly admitted into the Avengers without having those issues addressed. Mind you, in Quesada's Marvel, continuity is largely irrelevent, so they can just pretend Rogue was never a terrorist.