5.h3 is playable. The usual advice of "develop your pieces" is actually a shortcut for "do not lose tempi". Although 5.h3 does not makes anything to improve White's development, neither does the forced 5...Nh6 that follows, so White has neither won or lost a tempo here.
6.d4 (instead of Bxa6) : one exchange is usually a lot of material (between one and two pawns), I would have taken it. Not taking looks plausible though, because Black needs to lose another tempo by moving the rook if he does not want you to take it later.
7.Bb5 : the threat on the rook is not significant, but the fact that you develop a piece for free (tempo-speaking) is.
9.Bc4 (?) : 9.Ba4 ?? is not better as it loses the bishop after (9.Ba4) 9...b5 10.Bb3 a4 and you have no square. Hence the better after that is 11.Bxf7+ to destroy a bit the king's cover, and White should have some compensation for the piece, but only because Black's position was so terrible already before.
However, 9.Bd3 ! forcing the rook to move again was better.
12.Nxe6 misses :
13.d5 ??????????????????? throws away a pawn for absolutely no reason (one question mark for the pawn, the rest for the absence of reason). At your rating, you will improve a lot if you force yourself to justify every of your moves. Qh5+ with in mind the previous puzzle (though Black can escape to d7, but he will not survive long was better.
14.Nxd5 ?? throws away a piece. The check on b5 should have been easily parried with ...Bd7.
16.Qh5+ is no longer a good idea as the bishop does not attack g6 anymore. However, 16.Bxh6 gxh6 17.Qh5+ was maybe White's best.
22...Bb4 ?? is indeed hanging a piece. Even if Black thought that somehow it would make you move your e5-pawn despite the pin Bb7-e5-Qf3, 23.exd6 is on check (so that he cannot capture on f3) and 23.e6 Bxf3 ? (less worse ...Qc8) 24.exc7 is totally winning.
26.Rxd8 ?? is a huge blunder. Bxd8 instead gives a winning endgame after the trades 26.Bxd8 Bxf3 27.Bxc7 Bxe1 28.Rxe1 (one more rook, and the Nb8 will soon die), or 28.Qb3+ continues the attack (though I cannot see a clear line that ends up with win of material, White is completely winning).
29.Bxh6 is best - what check can you deliver without hanging a piece ? If e6+ Kg7.
30.Rd1 ? hangs the Re8, which your opponent did not take. Much more promising is 30.e6+ ! Kxe8 31.exd7+ where White should promote his pawn and win.
35.Kg3 ! is much better than Kh2 - it probably does not win the knight, but the black king is in a mating net and threats of Rd7 attacking the queen and the 7th rank are in the air. White should win this.
After the 36th move blunder, Black is much better, but not winning yet. 39.Bg3 is probably a draw (not sure).
41.Bxg5+ ?? gives a piece and with it all hopes for a draw. A "drawn endgame" ? When Black has a queen for a rook ? The queen is roughly worth 9.5 pawns (when a rook is 5). There is a forced win, but for Black ! It should have been longer than in the game, but it does not change it : you are dead lost.
Hi everyone this is my first time posting on this forum! would greatly appreciate it if you guys could help me improve! I have written down my thoughts on the game in the comments including some questions i have when playing the game and during my review afterwards.
And on a side note, what is the best way to improve my chess as you can see my rating is really very low and i would really like to improve. thanks alot in advance!