Bishop D-3
Belgrade gambit

I'm pretty certain, doing it in my head, that Q e2 wins outright. Black only has f5 after which Bg5.
White's still down two pawns and I don't see why Bg5 is such a good move.

I agree that it's maybe not a very practical choice from Black's point of view for an opening that you're hardly ever going to face; I'd probably play 5...Nb4 or 5...Be7 but I have seen very strong players take on e4, and then its a mess after Qe2 (as you say)
What do you think the next move should be ?