Arrogance? I think not!

So today at lunchtime I played a friendly match against a friend and as the bell rang I achieved what I thought to be a completely winning position (with mate threats). He completely disagreed and said my bishop was hanging (which it was, but he disregarded the fact that he was in check). I said that I had just played ...Qxe3+ and he couldn't take the bishop and he said I was being arrogant. Say what??? I mentioned that I had 4 pieces attacking his king with only his g3 and h2 pawns sheltering it and he said he had a queen and 2 rooks (which he had, but his queen and first rook were on e6 and d6 and his other rook hadn't done a thing all game on a1). So the position is below and I've made this into a puzzle for his best try at avoiding mate (which still fails).

If you can find a quicker checkmate in the 2. Kh1 variation feel free to criticise me, tell me, whatever. I just thought this looked flashy :)

If you're wondering about the other variations...

Also I got my king to b6 because he sacrificed his bishop on g6 for 3 pawns before I castled and he said I was dead because I couldn't attack him. He had already castled kingside and I had the semi open g and h files so I was thinking "is he a moron or is it all a joke?)

Anyways, I have no more time so I'll end it here. Happy 10th of February Day (made up) from Sydney, Australia :D