12...Qxf3+ as you gave is better, nay best even. Winning a pawn and the exchange is almost the game in hand.
15...Bb4 is also better. You seem to have thought this out. But the variation should read 15...Bb4 16. Bd2?! (better is 16. Re2, and if 16...Nxc3 17. Rxc2) Nb6! 17. Bg5 Nxc4 18. Bxd8 Rxd8 with the bishop pair for a rook and a winning position.
About 20...Bxd2 or Bxe4: The question boils down to, do you want to leave white with a knight or a dark bishop? I think white has a harder time with the knight in that he can't push the kingside pawns quite so easily as with a bishop, but it's hard to tell.
I'm not sure I like 21...Rhe8. Not when you have a loose bishop, pawn and king on the c-file. Perhaps ...Kb7 or something, as problems come after 22. Rac1 d3?! which shuts your bishop out of the game. White then can play with his kingside majority while your bishop is locked out.
It's amazing how few squares the light bishop has. Therefore (by the power of hindsight) 17...Ba4 18. Nc3 Bc6 may have been a better idea, putting the bishop usefully on the long diagonal, aiming at f3 and the king.
24...g5 is an idea to always at least consider (maybe not play) in endgames, particularly rook endgames. Sac a pawn to weaken enemy ones, then win the lot later if possible. Also if that doesn't quite work, Kb7-c5-c4/Ba4 is another plan. Either ram the c-pawn down the board, or retrieve your bishop (white can play b3 and your bishop is worse than a tall pawn.)
26...Bxb3? loses the exchange. So instead 26...Rd5 or 26...Rc4 holds the pawn and the position.
28...d2!? 29. Rd1 Red8 infuses some life into the position, for if 30. Rc2 Rb4, a subtle difference from your other variation.
30. Rc3 Rdd4 swiping the f4-pawn looks promising, not as bad as you might have thought.
I think a better defence is keeping your rook on e2 behind the potential passed pawn, while using your king and a-pawn to force clarifications. For example, 35...a5 36. Kd5 Rd2+ 37. Ke4 Re2+ 38. Kd4 Kb5 39. Rc7 Kb6 40. Rc3 (40. Rxf7 draws by just ramming the a-pawn, and white can only perpetual by Rf7-Rf8 against Kb6-Kb7) White's progress is oddly difficult, or probably I'm missing something.
42. Rd7+?? was fatal. It hands you the full point where you could previously have only drawn with good play.
The endgame I think is (just barely) defensible by black thanks to the outside passed pawn. White's threat of a passer on e6 is very severe, but black's active king and rook should be able to hold it.
Overall, an interesting game as advertised. Very enjoyable to analyse.
This game is the first one that I'm posting on chess.com for analysis. In this game, played with 15 min for each side + 10 sec delay, both of us made a lot of (hopefully instructive) mistakes, and I was very lucky in that my opponent missed some opportunities to win. Here are some things that I would like to improve on from this game. You don't have to address them, however, if you have other helpful suggestions!
-I feel like I did not get enough out of my opponent's kingside weaknesses early in the game (I only gained a pawn). While I could have additionally won a rook (see annotations), is there any way I could have improved my attack in the opening?
-I don't think that I made enough out of my passed d-pawn during this game. Could there have been a more effective way to use it (such as advancing the c-pawn to go along with it)?
-Throughout the rook endgame, I felt like I was severely losing due to the threat of creating a very advanced passed e-pawn. Was this assessement correct (with correct play on both sides), and if so, where were the mistakes on either side?
Thank you for your help!