This point isn't so important, but after 3.Nf3, yes, it could be a sicilian (if black captures on d4), but it could also turn into a french (if black plays d5 as in the game).
Moves 4, 5, 6, and 8:
Black can win the e4 pawn.
I agree 3.Nc3 was better. Depending on your preference, 3.exd is also a good move.
7.Bxf6
Not a bad move... but also you don't really have a choice because if you take the time to retreat it, black can win the e4 pawn. Because your main pawn chain in the center (b2-c3-d4) are on dark squares, this is your "bad" bishop, so in terms of long term assessment it's really no problem to trade it. The pawns cover many dark squares, and the pawns also get in the bishops way, restricting its movement.
8...g5
Black loosens his kingside. This is NOT punishable in the short term, but it's worth mentioning an not an ideal move. In the opening development of knights and bishops off the back rank, placing (and keeping) a pawn in the center, and castling to safety are the absolute priorities. Flank pawns moves should be minimized. Black's earlier pawn move c5 was fine because it's attacking white's center pawn.
10...dxe4
Not good, now white has a pawn in the center and black doesn't. This also brings white's knight to e4 forcing black to defend or retreat the bishop. You say black has a small plus, I say white has a small plus.
12.Qd2
You finished development first, good job. When this happens ideally you can open the position with a pawn break (like playing d5 here). However this is not possible right now, and black has no immediately target-able weaknesses, so he's ok. I just mention it because this is a common idea in many positions (lead in development -> then open lines).
13.Bb5
Hmm, your development is finished, so moving an already moved piece again isn't so bad, but I'd prefer you bring your rooks to the c and d files. Rook on the c file is an open file, and a rook on the d file supports your isolated pawn.
14.Bxc6
Well, you didn't have much of a choice, because d4 was under attack 3 times with only 2 defenders. The bishop pinned the knight though, indirectly defending your pawn. So it was best to capture the knight.
Also you weaken his queenside. Black's a pawn and c pawn are isolated pawns now, and targets you can pressure, so in the long term it's not a bad move either.
15.Qc2
That's the right idea, already attacking the weak c pawn. Black can win your d4 pawn, but tactics make it unwise (you could respond to 15...Bxd4 with either 16.Rfd1 or 16.Qxc6).
That said, 15.Qb4 looks even better because now black can't castle (your queen influences the f8 square) and you're threatening Nd6+ which would permanently deny castling.
16.Ne5
Again, this is the right idea, pressuring his weak pawn.
17.Nxc6
Unfortunately tactics make this capture a mistake. This is a very common tactic by the way, so it's good to remember and that is after a piece seemingly wins material, a pin can trap it there and the enemy pieces gang up on it. "Pin it and win it" as they say.
For that reason it's usually a better idea to avoid the pin by capturing e.g. 17.Qxc6 instead. However black has even sneaker tactics after 17.Qxc6 i.e. 17...Bxe5 18.Qxa8 Bb7 forking the queen and knight.
So for now the c6 pawn was immune. It was better to keep pressuring it with a move like 17.Rac1.
18.Nb4
You give it a "?" but this is a reasonable try, you're undoing the pin because the knight retreats and protects the queen at the same time. Unfortunately black can use the tactic "removing the defender" by capturing the queen (removing protection from e4) and then capturing the knight on e4
19...a5
Black should have captured the free knight on e4.
20.Nd6
Your piece is loose there, better was moving it to c5, which is a square that's called an outpost i.e. a knight anchored by a pawn on a square that no enemy pawn can attack. In other words, if the knight were on, c5 black can't force it to retreat.
21...Ra6
You say black is winning now, but the knight did have a safe square. It can go to b5
22.Ne3
You could have saved the knight with 22.Na5
23.Nxd5
You give this double ? but it's just a trade. True you don't want to trade when down in material, but it's not a huge blunder. Black has the same level of winning advantage either way.
Moves 24 and 26
This is going full passive defense mode. It seems like a good idea in the short term (you're defending your pawns right?) but in the long term the pawns are lost anyway because black will gang up on them while you wait passively. It's better to put your rooks on open files and to pressure black's pawns e.g. putting both rooks on the 7th rank to attack f7 and they can move to attack any of black's pawns from behind.
31...Be7
Black continues to refuse to capture the d4 pawn. It seems he didn't realize it could be won.
36.Rf2
Offers a trade of rooks when down in material, bad idea as this makes finishing the game easier on black.
36...Rd5
Black declines the rook trade when ahead in material. Bad idea.
37...Kh5
Loses the f7 pawn
39.Ra7
You give this a ? but this is at least the right type of idea. Your rook attacks from behind. This is better than passive defense when it was on b2.
Moves 40, 44, and 52 I agree with what you said.
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Overview of the game's lessons:
Observational mistakes on moves:
4, 5, 6, 8. 19, 22. 27-34, and 37 (material can be won right away, but one or both players missed it)
Tactical ideas on moves:
15 (black can't capture your d4 pawn because fork on c6)
17 and variations to move 17 (pins, forks, and removing the defender)
Strategic ideas:
7 (idea of a "bad" bishop)
8 (weakens kingside)
10 (gives up center pawn with loss of time)
14 (idea of creating a weakness, in this case isolated pawns)
15 (prevention of castling as strategic success)
15 and 16 (pressure on isolated pawn)
20 (outpost for knight)
23 and 36 (trading pieces when ahead (good) or when behind (bad)
26 (all pieces stuck on passive defense is bad)
39 (rook that has infiltrated attacks pawns from behind)
Please tell us what I did wrong in this game.
Any feedback bad or good would be much appreciated.
I am going to start on study plans, tactics and go back to basics like the idiot's guide to chess and how to beat your dad at chess.
I will check computer analysis and variations etc after people's thoughts cheers.