Yes, I preferred this to d6.

3. ... d5 4. BxP and black is back defending the f7 threat, but has lost a pawn in the meantime.

Looking at his next two moves I'd imagine he is still fixated on mate on f7, the subsequent g4 seems designed to lure your knight away from the protection of d5 so he can move his queen there. This is of course a terrible way to play chess...

Even by a naive concept, Qb3 would have been appropriate (bad because of Na4). Qc3 would have been bad as well, but the idea could have been to leave room for the Nf3 and press e4. The text move is hard to explain.

Your dsb feels free to go there because white can't use his own dsb to press on the Nf3. If 5.d3 instead of Qd3, now Bg5 comes, and black is kind of forced to use his dsb to defend f6 (Bg7 or Re7? because of Bh6 by white). His action is stronger here, however, than on the self-blocked g7's diagonal.

The idea is to be aggressive, and that explains the plan behind Qd3. In fact, it's a common mistake a player can do: see an attacking line, and be so enthusiastic about it to forget to see which are the opponent chances to defend... and "what will happen next"!  

Everything stops for check. I don't see a reason not to throw in BxP+ before playing Qf6. Black is two pawns up, white has a very open king and his attack is foundering. Black's next move is probably to castle, and the rest is technique.

After 6... Bxf2+, white is busted. Kf1 allows a discovered check and a tempo. Ke2 allows Nd4+, letting in another piece that threats c2. Kd1 and BxN makes f3 vulnerable for a Q check. The smart plan by white had a little "flaw": by diverting the N from f6, he is also creating a weakness on his own corresponding square.

Again, BxN or Bc2+ were better.

White tries desperately to create some countergame. He wants to get out his dsb without leaving black a tempo to play anything else than Bxd4. Unforthnately, black has many resources, like Nxd4, that gives white the choice about which piece to take, but with horrible consecuences in both cases.

There is not actually! Qxg5 Qxf7+ Kd8 and your king is surprisingly safe on d8 since the rook safeguards the back rank.

The sac is daring and imaginative, but it just doesn't work, even if black goes for it.

...and he got his objective: to divert black Q from the f column, and to make the lsb an active piece. Not enough, but look at the "psychological side": black was "scared" about QxB, but he had no real reason. Nevertheless, he acted just well: now, nothing can avoid a neat NxR.