Guidance With Tactis

It may help to solve tactics that have been groups by themes. That way it may not seem so arbitrary. Chess.com and some other sites go all out in listing tactical themes... so much so I think it's overwhelming for a new player and some are so esoteric I sometiems wonder why anyone would bother including it on the list. The main themes you should learn first are:
fork
pin / skewer
removing the defender / overworked piece
discovered check / discovered attack
Themed tactics of these and a few more can be found in this book if you're interested:
https://www.amazon.com/1001-Winning-Chess-Sacrifices-Combinations/dp/0879801115
As for what to do while playing:
1) Look for and calculate the forcing moves available to you. These are checks, captures, and threats. Especially captures and checks.
2) Be greedy. Don't sacrifice unless you see a way you definitely come out ahead. When something of yours is attacked (lets say a pawn attacks your knight), you need to defend against that threat (in this case move the knight away). I mention this because you sacrifice your knight with no followup on move 21 in the first game. Some new-ish players think being down a knight or bishop doesn't matter... it matters a lot! Be greedy.
3) This is like #1 except this time imagine your intended move as if it's already been made on the board and find all of the opponent's forcing moves. What can they capture? What are the ways they can check you? What are the undefended pieces they can threaten? If you still like your intended move, then go ahead and play it.
Here's a quick test. In your first game look at the position after black's 14th move (bishop takes knight). Now, without moving the pieces, imagine playing Nd4 (this was the move you played in the game). While imaging that knight on d4, can you find a black capture that wins something? I'll put the answer at the bottom of this post.
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Here are some example puzzles with the theme listed. I used positions from your first game when possible.
Discovered attack
Pin / skewer
By moving, the knight has left the e5 pawn undefended. Black can capture the pawn on e5.

I agree with Telestu: tactics fall into categories, so once you learn those categories you will be able to detect a certain type of tactic across a huge span of positions. Some categories I believe Telestu missed are: (1) the weakness of f7 (or f2); (2) Taking advantage of a center that has no impeding "Nimzovitch pawn" (at e6, d6, or even e5 or d5); (3) Hanging pieces. For example, 7. d5 Na5 8. Be2 not only seizes the center, but contains threats like Nxg5 ...hxg5 Bxh5 ...Rxh5 Qxh5.

Playing 15/10 games definitely helped me over just 10 minute games. Then I went to 30 minute games and improved even more. BTW, 30 min. games don't seem to take a whole lot longer than 15/10 games do for some reason it's just that you don't have the clock pressure. Lately, I've also been playing daily games and I find that the extra time really helps me make a better move. A lot of times, I will take a complicated position and set it up on my analysis board, going over it for a whole day before I make my move on the website.