Did they introduce Powergirl in the nu52? What's her backstory now?
Yes, in "Worlds' Finest" (introudced in the Second Wave.) Her and Huntress are from Earth 2 and got transported to the New 52 Earth during a battle between the E2Supers and (Apokalypse?), where they served as Supergirl and Robin (the daughter of Bruce Wayne and Selina Kyle.) On N52 Earth they're Huntress and Power Girl but have tried to keep out of the way of their counterparts and others in the super hero community, though they had a recent run-in with Damien Wayne. Huntress has used her knowledge of her "father" in order to get some funds/resources from Bruce Wayne, Power Girl has set her self up as a rich industrialist, funded between Huntress' funds and using her powers to raise funds.
Yes, Power Girl's suit started off as a full body suit but she's going to revert back to the Teddy w/Cape in an upcoming issue.