What mistakes am I making in this game, and what can I do to fix them?

I don't really analyse games. But looks like you are going for checks just for the sake of it when they aren't going to lead to anything. You wont get a checkmate with just one piece unless its your queen and they are blocked in or something. You can check them at times, but only if there is a reason IMO.

You blew your pawn structure wide open and over-extended IMO. Its good to advance on the board and take middle, but I like to keep one side of the board very tight and keep my king there (normally), but it is game dependent. You were very wide open and vulnerable to exploitation here. Focus the middle of the board, not the sides.

This is mostly irrelevant compared to all the blunders that throw away pieces for no reason. Moves like 3. e4 or 13. Bd3 or 15. Rg1 or 17. Rxg7 or 19. Nc4.

The OP should concentrate on avoiding one-move blunders like those. Nothing else is important.

Both are important. It's obvious white has no plan at all. He can and should think about things like king safety (why 7.g4 is foolish) and basic opening principles (why 4. Bb5+ is questionable and 5. Bf1+ is definitely a mistake) when trying to come up with a plan.
Blunders *will* happen to beginners. Knowing some basic positional principles can help to make blunders less likely. Without 7.g4 there would be no 15.Rg1 or 17.Rxg7. (the first is a mistake, the latter a blunder.) A wide-open position is just asking for trouble.
But you're right, it's the blunders that are truly decisive. Move 13 was one blunder. I've mentioned 15 and 17. 19 is an egregious blunder. White also missed one-move captures: the rook on h5 could have been taken by the bishop on move 18 (and the fork that enabled that should have been made one move earlier instead of throwing away white's rook). For his part, Black missed a mate in one on move 27, and I'm sure there was more.

No, not "both are important" at OP's "level" (which is just no level at all).

And yes OP must first focus on pieces that can be taken for free, on both sides.

Once this became a habit, OP can go learn other things.

Ideally, it's time to move to learn more things, once you begin to lose games without seeing why nor how, even after reviewing your game carefully.

I've seen chess players who can babble for hours about some odd variation of some secondary gambit within a rare opening, but can't play a single game without bludering a piece. THAT makes no sense. At all.

First things first.