Is this a mistake?

Here http://en.lichess.org/training/2399 I played bf4 and when I played the move it ended up the same: a queen for a minor.

No idea.

depends on the scenario. You didn't give much information to go on. But, a queen is definitely better than a minor piece.

its not a mistake, its winning for black but u cant play cheap moves afterwards if u play a strong opponent such as stockfish
for example
http://en.lichess.org/1nUGzIcu/black#125

# Stockfish agrees, about the same score for both moves :
At depth 27/48 :
-4,66 8. ... Bc5 9.Qxb7 Bb4+ 10.Bd2 Bxd2+ 11.Kxd2 Qxb7
-5,94 8. ... Nc6 9.Qxb7 Bb4+ 10.Bd2 Bxd2+ 11.Kxd2 Qxb7

Although both moves work out pretty well, I think the knight move given in the solution is slightly more natural, because it puts pressure on the central pawn after developing a piece.

I agree with this being a problem though. (that Bc5 fails the puzzle)
I like the way chesstempo did that (and I think lichess should adopt that): If you play a suboptimal move that is still winning (like here, e.g. everything above +2) you always get a "try again".