What is the best way to improve understanding of strategy and endgames?

To some extent middlegame and endgame strategy is pattern recognition, but initially the best way is playing over well-annotated games by the old masters (even master games without annotations are great for giving you an intuitive feel for where the pieces go).

You're wrong at all your statements :

1) You can play any opening you want, but not every variation is recommended for beginners.

2) I'm not a professional coach. I said that you need to find a coach, that's all because it's really hard to become good at chess without a coach. I just stated that I can do it myself. Anyway you can find another person. I didn't insult you, you are just thinking that the truth is offensive but the truth is the truth.

3) Algorithmic trading earns more money than any bank. You need to be a genius and be rich to create a company which runs a program which implements an artificial intelligence that will trade for you on many, many servers.

If you (OP) are in fact interested in a coach, please take a look at my profile and send me a private message if you want to see rates and options. Also feel free to read my article from Jan 29. User SmithyQ has taken lessons from me and can provide a reference.

I'm sorry, may be I was too rude but you've made not the best move by asking people to do all the work for you. First you need to make a research by yourself and then ask for help and showing your thoughts on the problem. You know, I'm not your secretary and I'm not your mom, so I'm not going to spend hours explaining the problem for you because you didn't make a research. Also I don't even need that groschens 10 dollars. I just made the price which can be affordable for everyone who is interested in chess.

"I could probably do this research on my own, but I would like to know from you players out there, how did you go about improving your strategical understanding?"

Different things work for different people.  And since you made no effort to include what your study regimen is?  Or included any games with your own analysis, so we can get an idea of your thought process, and what you need to work on.

Lets take a look at your last game...

 Finally some constructive criticism.

The best way to get a better grasp of strategy, in my opinion, is to play over annotated master games and see how they make strategic decisions.

There's no quick way to "get better at strategy", unfortunately, because there are various different plans in different pawn structures, and many choices you can make.

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Looking at the above game^ you posted, the pawn structures determine the plan - on moves 9-10, you should just finish your development - this is usually correct when you don't know what to do, particularly in non-closed positions. However, in the game above, just naturally developing is not that good.

The plans depend on the pawn structures - in the above pawn structure, notice that if you put a knight on d5, it's a strong knight, and if it gets traded off, you can do exd5, and suddenly you have a backwards pawn on e7 to attack, which is good for you. 

So instead of Nbd2, you could've played c4-Nc3, developing the knight on a better square - preferably you play c4 on move 8, because of ...Ng4 ideas.

Also, Nbd2 allows black the "positional tactics" ...Ng4, winning the Bishop pair. 

Later on in the game, black created a weak d-pawn, which could've been targetted.

These are all typical strategic ideas in this kind of pawn structure of the classical sicilian. It's not something you can learn in one day, so I just recommend playing over a lot of master games and seeing how they think.

Good luck.

P.S: Here are some very general tips that I think can give you a better plan in most positions:

(1) If you don't know whether to play in the center or on the flank, play in the center.

(2) If your opponent has a weak pawn, and you don't know what to do, try to target that weakness.

(3) If you don't know what to do, generally you should complete development, and improve your worst placed pieces.

Tried to insert a game with comments. 

 I don`t play much blitz anymore, I play mostly 15 min with 10 second increment. Blitz is a different game IMO. Sometimes I play blitz for fun and when i dont have time for rapid

"This is called "Hope Chess" and its a really bad way to play.  Hoping your opponent doesn't see the right moves."

With all due respect, "Hope chess" is making moves without considering opponent replies - it happens almost regularly with sub-1600 players. Term used by Dan Heisman.

Making bad moves, hoping your opponent will make worse ones is closer to "hopeful chess". 

"With all due respect, "Hope chess" is making moves without considering opponent replies "

Thats what i just said.

Hopeful chess implies there is a "right move" - a move that completely refutes what you're doing.

Hope chess is a general way of thinking, where most of the time you're OK, but sometimes you get destroyed by a tactic you don't see. 

Another game with comments

 I was not actually trying to play "hope chess" with that discovered attack on the knight. I simply did not see that my d3 pawn would be hanging after the exchanges. I saw it afterwards when I went through the game. 

I like your analysis of my white Sicilian game, playing the prophylactic move h3 before playing my bishop out is a very helpful idea. The idea of moving my queen towards the kingside as a general idea is also eye-opening. I make the mistake of trying to create something too directly.

moving the b pawn up in the Giuoco Piano game to attack the dark square bishop also seems much better than passively trying to hide my bishop away

A lot of the comments here (especially by DaniilKalabukhov) are quite toxic and rude. The OP had the humility to come here and ask for help, admitting that he has has flaws in his game and he wants to improve, so is there really a need to be so condescending towards him, telling him that his own analysis of the game is "terrible" and that he's somehow undeserving of our help?

I'm going to start this off more positive: Giasira, I think you have pretty decent tactical skills, you have a decent positional understanding and you seem quite good at spotting weaknesses. It's also great to hear that you're playing slower time controls like rapid games and watching guys like IM John Bartholomew on YouTube. You're definitely heading in the right direction if you want to improve your game.

Now some areas I think you could improve on are:

1) Knowing when to trade pieces (particularly trading knights and bishops) - in general, you seem to be quite hesitant to trade your knights for your opponents' bishops. But in most of these spots, the bishops have more value than the knights, so you should be happy to make those trades.

2) Moving the bishop too many times before finishing development - in general, knight maneuvers should come earlier in the game, whilst bishop maneuvers should come later in the game. You often waste a few tempos maneuvering your bishop around, only to find that the new bishop position isn't even that much better than the old position, and you could've used those moves to develop other pieces instead.

3) Forgetting to move your king to the h-file when pushing the f-pawn - As a general rule, you want to move your king towards the corner of the board if you're going to push your f-pawn.

I will show you 2 random positions where I felt that you could've made better strategic moves:

Position 1: finishing your development the right way.

Position 2: tactical way to win a free pawn.

I hope this helps!