You play much, much better than your rating indicates it, and your opponent a bit better.
8.Nxe5 ? is bad. After accepting the 'trap' 8...dxe5 9.Bxb7 Nd7 10.Bxa8 Qxa8 White has a rook and a pawn for two minor pieces, which is already a bad trade in most situations and even worse in the middlegame, and Black's queen eyes a diagonal through the weakened kingside.
16.Qf3 (?) gives Black a bit of counterplay. I would play Bd4, and if Black founds the correct ...Bh3 (accepting the trade is suicide, Black is left with a material deficit, a bad bishop and nothing to attack) repeat the position once by (16.Bd4 Bh3) 17.Bg2 Bf5 18.e4 and follow by flooding the center with your pawns.
18.Qb3 ? : When ahead in material, you generally want to trade the pieces, especially the queens. Here I guess you were afraid Black's pawns could become a threat, but after 18.Qxd4 cxd4 19.e3 (there are other plans, for instance place the bishop to b2) 19...d3 20.f3 and d3 becomes horribly weak, which means White will win one more pawn, with an easy win.
21.Rab1 (?) : again, there is no reason to refuse to trade material here. Black's f5 bishop is blocked by his own pawn which makes it a terrible piece in the endgame. -> Bc3
22.Rfc1 ? was indeed wrong, for tactical reasons : 22...Bd6 ? missed ...e3 ! and Black gets back in the game by winning an exchange. Whtie has still plenty of play and compensation of course, but that's still better than dead lost as in the game.
29.Bxf3 ? HUH ! you need to know what you are going to do before playing such moves with cold blood. Imagine a moment that Black's queen was on h3, how do you prevent the mate ? You can't. And what can you do to prevent the queen from going to h3 ? you need to play your own queen to f1 in time - which means you greatly restrict your options.
But I am not worried, you will mate and get mated plenty of times by a pawn on f3/f6 and you will learn.
After move 38, the rook endgame is a good deal better for White, robably winning. By decreasing importance, his rooks are more easily developed (= active) ; the d5 pawn is passed (with serious queening prospects) and protected versus h6 that is isolated (=weak) and facing the white king ; and his king is a bit unsecure.
39...Kh7 ? accepts the loss. Activity is absolutely needed, for instance ...Rb8 and then ...Rc2.
48.Rc6+ : "Rc7 was better" : yes, but still not optimal compared to Rd5 followed by c4-c5-c6-c7. The white king can stop the h pawn in time.
After 50.Kg1 ? it looks like a draw to me. After 57...Ra2 it is clearly a draw : the a pawn falls, and the black king is in time to stop the c pawn.
However, there are still winning prospects after 57...Rc2 ? before 60.Rf1 :
In the game Black did not rushed his king towards the promotion square, which would have made the draw hard to obtain after 68.Kb5 ! (instead of a4 after what the black king can advance). Another typical endgame pattern : "shouldering" when you maneuver the king to block the opponent's.
I realise my endgame technique requires some polishing. Feedback and pointers very welcome.