Losing to level 2 as a beginner -

Thanks for the inputs!
I have actually done quite a bit of counting myself, as I noticed by myself that this approach was a basic principle. It has felt quite primitive to sit and count, but primitive if obv. not bad in itself.
No doubt I have made many counting mistakes in my games, but the 10minute games are still very fast for me. 

Now I tried to focus a bit more and apply some of the suggestions in a live game.

It worked out very well, as I see it. The ending was obviously kind of horrible. I remember that the game is a draw if the opponent is not in check but can't move, so I wanted to avoid that. I had plenty of time though, so no need to end it this way.

I'm playing as black there.

At least now I know the answer to the question “what’s the most generous draw you’ve ever seen given”

38...Rg3# (among others) In fact I don’t think there’s a rook (e3 rook) move that ISN’T mate lol 

6. ..d6 - supports the knight and puts pressure on the rook on h3; generally, if a move accomplishes two things all at once, this move must be considered. 

8. ..f6 - No! f7 is initially the weakest square on the board, and you should always be wary of moving this pawn in the opening. Exceptions to this rule of thumb do exist, for instance if you're playing King's Gambit as white. Probably healthier moving the knight yet again, even though that breaks the principle of "democratic development". It is, after all, a Knights Tango we've got going here

13. ..Nc2 wins a nice rook and the white king will never castle.

20. What would you have done if white had simply played f7? 

38. ..Rg3# with an endearing double check. 

From your second game against a human playing Black.  Quite instructive.

Thanks for the feedback once again!

@JamesColeman haha well yes, there you go. Glad I could help.

@total_oblyst I'll have to go over those comments again, thanks

@Clavius thanks for the elaborate response. I'm playing as black though. But I'll go through it.  

Så lidt da  Jeg glemte at nævne, at dit spil ser lovende ud; du skal nok blive til noget, når du først har fået lidt rutine. 

A few additional comments from Black's point of view.

Bear in mind on your latest game that you played against someone who was not skilled enough to challenge the ideas given in the earlier posts. For example, your opponent was silly by throwing pawns up on the board and forcing you to move your knight all over the place. As a result, he was dropping them like flies and you could not take advantage of ideas like "not moving the same pieces over and over" and "castling early." You should try again and record a game where your opponent has some theory in mind when playing rather than just tossing stuff on the board and seeing what sticks. You'll have a much better game by playing someone at your skill level or better. It's kind of a waste of your time to need analysis of a game where the "best" or even "just good" moves are important, because your opponent probably wasn't going to find or capitalize on your bad moves in the first place.
That being said, you definitely had a win in that game, and I give you credit and a congratulations for your success, even if you decided to accept a draw instead.

Just played this game. Seems to me like I was outplaying him, but time is brutal when you haven't played much chess and haven't automatized every move
https://www.chess.com/analysis/game/live/3942329581

Take a look at this line where you attack and win vs retreating your knight at move 10:  

Thanks again for the inputs. I have read through it, and will do so again.

I can't seem to figure out why Knight is preferred by engine here?

Wins material due to the idea of Ba5 mate. 

CM Coleman is quite right.   What you need to see in this position RainyHideAway, is that the black king is completely encircled, trapped.   It's called a "mating net".   It's a goal to be planned for, to take away all escape squares before delivering the knockout blow.  ANY check therefore is mate presuming the checking piece can't be taken or blocked.   When you see a king in this position, you should look for checks, Once you have this idea and see this in a position, then you ask, where is the check, and then the Ba5++ becomes obvious, and to do that you've got to move the knight first and you can threaten the undefended bishop giving black the choice of stopping the threatened mate with a5 or saving the bishop and losing.   Learning to see these things takes time, and here's where the coaching comes in; you asked but didn't see why the knight move was best; so would you ever have found it on your own?   Or, the useful comment of CM Coleman acting as coach showed you the way quickly.   This is why I recommend in person lessons with a good coach.   Good Luck.

"... for those that want to be as good as they can be, they'll have to work hard.
Play opponents who are better than you … . Learn basic endgames. Create a simple opening repertoire (understanding the moves are far more important than memorizing them). Study tactics. And pick up tons of patterns. That’s the drumbeat of success. ..." - IM Jeremy Silman (December 27, 2018)
https://www.chess.com/article/view/little-things-that-help-your-game
https://www.chess.com/article/view/how-to-start-out-in-chess
https://www.chess.com/news/view/a-new-years-resolution-improve-your-chess-with-new-lessons

https://www.chess.com/article/view/mastery-chess-lessons-are-here
"... In order to maximize the benefits of [theory and practice], these two should be approached in a balanced manner. ... Play as many slow games (60 5 or preferably slower) as possible, ... The other side of improvement is theory. ... This can be reading books, taking lessons, watching videos, doing problems on software, etc. ..." - NM Dan Heisman (2002)
https://web.archive.org/web/20140627084053/http://www.chesscafe.com/text/heisman19.pdf
"... If it’s instruction, you look for an author that addresses players at your level (buying something that’s too advanced won’t help you at all). This means that a classic book that is revered by many people might not be useful for you. ..." - IM Jeremy Silman (2015)
https://www.chess.com/article/view/the-best-chess-books-ever
Here are some reading possibilities that I often mention:
Simple Attacking Plans by Fred Wilson (2012)
https://web.archive.org/web/20140708090402/http://www.chesscafe.com/text/review874.pdf
http://dev.jeremysilman.com/shop/pc/Simple-Attacking-Plans-77p3731.htm
Logical Chess: Move by Move by Irving Chernev (1957)
https://web.archive.org/web/20140708104437/http://www.chesscafe.com/text/logichess.pdf
The Most Instructive Games of Chess Ever Played by Irving Chernev (1965)
https://chessbookreviews.wordpress.com/tag/most-instructive-games-of-chess-ever-played/
Winning Chess by Irving Chernev and Fred Reinfeld (1948)
https://web.archive.org/web/20140708093415/http://www.chesscafe.com/text/review919.pdf
Back to Basics: Tactics by Dan Heisman (2007)
https://web.archive.org/web/20140708233537/http://www.chesscafe.com/text/review585.pdf
https://www.chess.com/article/view/book-review-back-to-basics-tactics
https://static1.squarespace.com/static/5856bd64ff7c50433c3803db/t/5895fc0ca5790af7895297e4/1486224396755/btbtactics2excerpt.pdf
Discovering Chess Openings by GM John Emms (2006)
https://web.archive.org/web/20140627114655/http://www.chesscafe.com/text/hansen91.pdf
Openings for Amateurs by Pete Tamburro (2014)
http://kenilworthian.blogspot.com/2014/05/review-of-pete-tamburros-openings-for.html
https://chessbookreviews.wordpress.com/tag/openings-for-amateurs/
https://www.mongoosepress.com/catalog/excerpts/openings_amateurs.pdf
Chess Endgames for Kids by Karsten Müller (2015)
https://chessbookreviews.wordpress.com/tag/chess-endgames-for-kids/
http://www.gambitbooks.com/pdfs/Chess_Endgames_for_Kids.pdf
A Guide to Chess Improvement by Dan Heisman (2010)
https://web.archive.org/web/20140708105628/http://www.chesscafe.com/text/review781.pdf
Studying Chess Made Easy by Andrew Soltis (2009)
https://web.archive.org/web/20140708090448/http://www.chesscafe.com/text/review750.pdf
Seirawan stuff:
http://seagaard.dk/review/eng/bo_beginner/ev_winning_chess.asp?KATID=BO&ID=BO-Beginner
http://www.nystar.com/tamarkin/review1.htm
https://web.archive.org/web/20140627132508/http://www.chesscafe.com/text/hansen173.pdf
https://www.chess.com/article/view/book-review-winning-chess-endings
https://web.archive.org/web/20140708092617/http://www.chesscafe.com/text/review560.pdf

You seem to me to suffer from reluctant-to-try-to-use-the-bishops syndrome.

King safety! I suggest you adopt a policy of always castling. Develop you kingside pieces and castle on that side, and you will get better results. Notice how in this game you had severe troubles on the kingside. Also leave your kingside pawns on their original squares.

Of course, if your opponent plays like a lunatic, he can prevent you from castling, but at this stage of your chess development, make castling a priority.

You're getting a lot of advice here, perhaps too much to digest.   For a beginner, Fred Reinfeld's old book THE COMPLETE CHESS COURSE, is a terrific book.   It was originally written as 8 stand alone books, and then combined into one big book.  IF you know everything contained there, then you'll be at a great starting point to begin to understand the game.   Book two of the volume is:  The Nine Bad Moves, with chapters on Neglecting development with many game examples of good play vs bad play; exposing your King to attack; making too many Queen moves in the opening; weakening your castled position; failing to guard against captures, getting pinned.   good luck.