@1
"about castling and when it would be best utilized" ++ Early and often.
"I am doing puzzles" ++ Good, but overrated.
"reading" ++ Chess books are no novels, do not read them, but study them, preferably with 2 chess sets: one for the main line and one for variations.
"lessons" ++ OK, but key is to play and analyse your lost games to learn from your mistakes, so as to avoid them in the future and to exploit similar mistakes by your future opponents.
@1
"about castling and when it would be best utilized" ++ Early and often.
"I am doing puzzles" ++ Good, but overrated.
"reading" ++ Chess books are no novels, do not read them, but study them, preferably with 2 chess sets: one for the main line and one for variations.
"lessons" ++ OK, but key is to play and analyse your lost games to learn from your mistakes, so as to avoid them in the future and to exploit similar mistakes by your future opponents.
Thank you for your feedback.
Not to be rude, but I am specifically asking for help with that last point, which is why I posted the game that I lost into a game analysis forum.
And obviously I'm not reading chess books like novels. I spent multiple hours on individual games of the book I'm reading for the sake of learning. Studying is implied when one says reading.
I put all of those caveats in so that people would help with game analysis of the match that I posted; If people don't do that here I'm happy to delete the post! The problem is I castled as early as I thought I was able to, and it was considered a mistake. Would like feedback on that if possible.
@3
In this case it is obvious that taking the rook 12 gxf3 is better than castling 12 O-O.
Of course 4 Nf3 is stronger than 4 Nh3: the center.
6 Qf3 commits your queen too soon. If he plays 6...Nc6, then he can harrass your queen with ...Nd4.
7 O-O was a good time to castle. 7 Ng5 plays a piece for the 2nd time while you have undeveloped pieces on their starting squares.
8 Bxf7+ is a bad trade: You give up a developed knight Ng5 and a developed bishop Bc4 for an undeveloped rook Rf8 and a pawn f7.
9 Nxf7 is obvious. 9 Ne6 Qe7 leaves you behind in material
10...Qd8 would have won for black: the knight Na8 is lost.
@3
In this case it is obvious that taking the rook 12 gxf3 is better than castling 12 O-O.
Of course 4 Nf3 is stronger than 4 Nh3: the center.
6 Qf3 commits your queen too soon. If he plays 6...Nc6, then he can harrass your queen with ...Nd4.
7 O-O was a good time to castle. 7 Ng5 plays a piece for the 2nd time while you have undeveloped pieces on their starting squares.
8 Bxf7+ is a bad trade: You give up a developed knight Ng5 and a developed bishop Bc4 for an undeveloped rook Rf8 and a pawn f7.
9 Nxf7 is obvious. 9 Ne6 Qe7 leaves you behind in material
10...Qd8 would have won for black: the knight Na8 is lost.
Thank you!
Like I said, I've only been playing for a week, so it is helpful to have the fundamentals reinforced through mistakes.
I.e,
1. one move per piece in the opening
2. trade quality not only includes piece value, but development (I'd only heard this once before you said it again)
3. Not being hyper-fixated on your own moves to the detriment of your position.
You can't learn from mistakes you don't understand! Thanks for pointing things out 
I hope you have a good one.
One of the main problems with your combination (starting with Bxf7+) is that it doesn't work. The other main problem with the combination is that it's too complicated. In a long line it's easy to make an elementary mistake.
My advice is to concentrate on the most basic things. If you can take a piece for free, take it. (Example: move 12.) Also, don't hang pieces yourself. These are the only things that matter. Don't overcomplicate things, play simple chess.
I can see that you have reached 1100 rating in puzzles. This is very good progress for your first week, So keep going and aim for 1200 then 1300 etc. As you get better at tactics, the number of mistakes you make in your games will reduce and you will win more games.
At the beginner level, and even at the intermediate level, tactics are the most important thing.
One of the main problems with your combination (starting with Bxf7+) is that it doesn't work. The other main problem with the combination is that it's too complicated. In a long line it's easy to make an elementary mistake.
My advice is to concentrate on the most basic things. If you can take a piece for free, take it. (Example: move 12.) Also, don't hang pieces yourself. These are the only things that matter. Don't overcomplicate things, play simple chess.
You're 100% right. I've been doing a very bad job of this over the past two days. I've been shaken up a little by some weird openings played by my opponents and let it get to my head. Will make sure to redirect myself ASAP.
Would love feedback, particularly about castling and when it would be best utilized in a game like this (the best move seems obvious now, in hindsight)! Some initial thoughts from a newbie who has been playing (AT ALL IN THEIR LIFE) for a week.
I'm posting in "game analysis" for a multi-pronged approach to learning chess since I don't have a coach. I am doing puzzles, reading, and lessons every day as well.