^EDIT^:Can`t be bishop. The position before Ba2+ is an auto-draw, mate with one B is not possible.
Is this position legal?

If the problem doesn't state that it's a Chess960 game, then it's considered from a usual chess game; if it's illegal in a chess game, even though it's legal in some Chess960 game, it's still illegal.

Looks legal; retract -1... Rb5xPd5 and now it should be easy to shuffle the pieces back to position. (No, the en passant is not forced; instead, it's the capture on d5 that is forced, either last turn or the turn before it.) One promotion is there, most likely promoting on b1 or d1, but there are spare captures to fiddle around. Blocking f7 with Black's units (on e6, f6, g6 for example) should be easy.

Here is what I guess the position would have looked a few moves before.
White had a pawn on c2, Bishop on b1.. Black's c3 pawn was on d4, Rook on b5.
White plays Ba2+, black replies with Rd5+, white plays c4, black captures c4 en passant and hence we get the position.
Cool! My thinking for last move was: