OMG it is a gift of a Trojan house made of paper

the nice thing about paper is that it burns up fast!

Not so good because 18. ...Be6 19. Bf3+ Kc7 would retain the powerful bishop pair.

 , Looks dangerous doesn't it. However, it should take only a minute at most to see 20...Nbc8. Then white has only 3 attacking pieces, and it cannot win. Here is an important tip in which you can improve your play immensly: When your opponent makes an apparent threat, always treat his threat with absolute contempt. This psychological trick helps to find refutations. If you lose this piece, there really is little point in playing on the game, so you should take a huge portion of your time to wriggle out of this, or at least complicate matters a lot.

Nbc8 protects the knight doesn't it?

It protects d7 not the knight. the real threat of Bc5 is that it allows white to capture the LSB

So easy! I'm ashamed, I didn't see it. Now it is crystal clear...  

Although you didn't find the best move, which saves the piece, you resign yourself to the opponent. Why play a move that you know will lose once you play it(OK, the opponent didn't find it here, but it really is very easy. Maybe he suddenly lost his concentration)? Instead, 20...g5 21.Bxe7 gxh5 22.Bxd8 Rxd8 gives you the advantage still. Or check this out: Even 20...Be6 can work, since the h4 knight can be trapped 21.Bxe7 Rd7 threatening both g5 and taking the bishop! I have a strong feeling you are having the advantage in all of these lines and more. Basically, if you don't see the backwards move to save a piece, you should not surrender to the opponent.

Completely right, tiger... remember it was a 3/10 blitz...  

Your opponent is right, you don't. But he did not see the reason why.

The opponent will explain. I thought that if I did BXd5, he would respond with RXd4, not realizing that I could then do BXe7. That's why I avoid speed games. I don't catch things fast enough, and here the clock was under a minute.

ab15, as you saw, I wasn't so good nor at the game or the post-analysis...  ))

The best technical win could have been achieved after 24...c3, and the pawn majority is frozen and c2 is threatened. Your knight has an outpost on d4. The move I would have done in a heartbeat.

Black has an absolutely winning advantage here. The extra material(the extra piece) will inevitably pick off more pawns, increasing the material advantage.