in your line with 18. Ka1 c1=Q+ 19. Bxc1 black can reply Nc2+ instead of Rxc1+
in other words, your queen sac was almost sound - worst case you are only down a pawn.
creative game - a nice case of courage being rewarded with fortune.
Sicilian Win (includes unusual queen sac!)
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Good point -- must've forgotten to look at that line.
It looks like a very nice sac. I haven't checked with an engine, but I think that after 18.Ka1 Rfxd8 you're winning.The threat is c1Q and Nc2 and if 19.Bc1 black has a formidable attack for a small material deficit. Here is a sample line I looked at: 19.Bc1 Nd7 (this knight will join tha attack via c5 and there is little white can do) 20.h4 Nc5 (threatening Nxb3#) 21.Bc4 Rd4 (threatening Rxc4 and Nb3#) 22.Qc3 Rd1 and now the rook can't be saved, because 23.Rh3 (23.Rxd1 cxd1Q is no good) Rxc1 is mate.
White's first mistake was 12. O-O-O?, allowing 12. ... d4!, forking his minors. 13. Qe1? not only does not save the position, it is actually inferior to accepting the loss with 13. Nxd4, so he won't also get the doubled b-pawns and the exposed king that ruin him later.
After 14. cxb3, you should have just moved your queen to win white's bishop for a pawn. Engine analysis confirms this to depth 19. After 14. cxb3 Qb6! 15. Bxd4 (15. Nd5? Nxd5 16. exd5 Nb4! 17. Bd3 (17. Bd2?? Rfc8+!, winning the queen) 17. ... dxc3) 15. ... Nxd4, you are definitely winning.
After 16. Kb1, you again could have won a minor with 16. ... Qc7!, since white's knight is stuck there due to the threat of Qc2+! Ka1 Qxb3, and white's only way to stop the mating threat is to trade his queen for the black knight.
According to my engine, 16. ... dxc3? was a bad move that equalized the position for white (depth 20). Of course, after 18. Kc1??, you are right that white is lost, and in fact you both played the rest of the game correctly. However, after 18. Ka1! Rfxd8, it is about even. (Black should play 18. ... Rfxd8, because after 18. ... c1(=Q)? 19. Bxc1 Nc2+ (anything else loses big time) 20. Kb1 Nxc1 21. Rxc8 Rxe1, white is up a pawn and has the bishop pair, while after 18. ... Rfxd8, the position is relatively equal, perhaps with black maintaining a small advantage.)
There were a few other moves that were probably inaccurate, but I didn't bother worrying about them. I also didn't bother analyzing the opening because I don't know much about that opening and all the moves seemed at least reasonable for both sides to me.
Granted, my opponent did not make the best move for the situation, but nevertheless, I gained the point. My notes are added. Any other analysis/insights are welcomed, especially from those who have an engine at their disposal to critique the line I chose, and the possible refutations from White.