Actually took my time with each move for this one. Tried following opening principles and playing defensively and I'm still getting rocked. Analysis even said I didn't blunder any either. Is it possible I'm just unlucky?
15. Ne2 is a serious mistake. You lose a central pawn for nothing, and it was really difficult afterwards. On top of that, the plan to exchange knights wasn't good in the first place. Nxe4 pretty much sealed the deal. The opponent gains a strong pawn center and it was all downhill, because it is like you are playing the rest of the game on hard mode, and the opponent plays the game on easy.
You followed opening principles and at least you weren't lost after a few opening moves. Play more games like that, and you are bound to win some, because in some of them the opponents will be the ones making more mistakes.
Best of luck.
If you don't go for the plan of exchanging the knights, the knight will stay on d4 and be very annoying, maybe you propose the plan of eventually playing c3 kicking the knight? Black probably first had to save his light square bishop since after 14.. Qc7 black is threatening to trap it. The only square for the bishop is on e2 really, and Be2 probably isn't bad because it stops Ng4 and it makes Nh5 suspicious). After that the black has a plan of launching an attack on the kingside and he already has a phenomenal knight on d4. I think white needs to play precisely there or he will be blown off the board.
When it comes to how this game went, sure, white blundered a central pawn, but he is 600, games between 600s are not decided by somebody blundering a pawn. 12..c6 was a high level move by black. Black (who is also rated 600) didn't make a single bad move the entire game, he punished white for all of his mistakes, he played 16..a6 at the right moment to kick the bishop either to now passive (but probably correct) e2 or to d3 where bishop is a target after Nf6 preparing e4 with tempo and attacking d5 pawn. On move 19 not grabbing the pawn immediately, but first playing the more precise e4 not allowing white's bishop to go to e4, killing activity of white pieces and grabbing more space. On move 22. his opponent played the ultra precise Nc3 instead of the obvious Bxa1. This is a model game by black. I don't know what happened in that game, but I am pretty sure that game wasn't played by a 600 for black, maybe an older brother, a friend, maybe he was smurfing, or maybe he was straight up cheating.
Damn, it took me 10 minutes to write the message then one misclick happens and it is all gone.
I will be short this time. Yes, it was better to go for c3 at some moment to deal with the knight. This move actually gives black an advantage equivalent of a minor piece. Perhaps it is not as straightforward, but it really looks bad. It looks like one of those games where it is much easier to play from that moment.
As for 12. ...c6, it looks good to me, challenging central control, but actually engine doesn't like it and gives +1.4 advantage to white after that move.
I agree that black played very well, but I am not sure if he was cheating. I am not sure, that is all. In any case, it is best to avoid such discussions here, because mods will just lock the topic because of it. The best is to just report it and move on.
Besides, in the grand scheme of things, it is irrelevant for OP. In my experience you will get a cheater once every 20 games or so, maybe 30, and they can't really stop him from improving. In any case, he did some good things in the opening, he should continue doing them and try his hardest not to turn over material for free.
When he is able to do it mostly every game, he will get a lot better.
I think he plays too many games however, I know that my brain would be fried if I've played so many longer games per day. Much better to play one or 2 and then look what was good and what wasn't.
Over the board. It means playing chess in real life instead of playing on the internet.