Center pawn strategy in the early opening phase

I often very early in the games need to make decisions on how to manoeuvre my pawns in the center of the board. When should I advance push, start an exchange or just leave the pawns like they are?

When I analyse my games often I see that I made the wrong decision. And often I can not understand why one move is  considered better than the other.  And since my memory is rather weak, I do the same wrong decisions over and over and never really improve

I don't really have the ambition or motivation to memorize opening lines, but are there any basic principles that you can  apply when trying to evaluate the position for the center of the board in the very early opening stage? For example after a possible exchange with equal loss of material, how can I see if my position has improved or not? 

I'm sure there are lots of theory available but the internet pages or the YouTube material I find don´t explain the theory behind the pawn moves for the different openings. And like I said I find it difficult to memorize moves, especially if I don't understand why they are considered to be good moves. I know center control is an important factor but often I feel I need some more criteria to base my decision on.

Typical situation could be like this position in the attached screenshot. In this case recommended move (pawn to d5), which lead to equal number of attackers and defenders on d5 and possible start of exchanging pieces.

(And it relevant for any adavice, I  am a beginner with 1000 rating on chess.com rapid)

(And

There's something odd about this position! If it was actually Black to move, the obvious--and best!--move would simply be 1...exd4! Winning a heathy piece for free. So I assume it must be White's turn. In that case, 1.N4b5 d6 2.Bg5 looks very strong for White. I don't want to nitpick, but the details of the position matter a great deal!

Orange indicates the move that I made, green arrow the computer recommendation.

But I was not realky asking about this specific position (even though you are free to comment on this too) but rather on a more general level how to evaluate the positions after the first opening moves regarding the center pawns, and when to start an exchange of pieces.

The problem with general rules is that chess is a very concrete game, and a general guideline may, or may not, apply, depending on the exact configuration of the pieces. 

That said, I don't see how the diagrammed position is possible. after 1.e4 c5 2.Nf3 Nc6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 it would be Black's move. In your diagram, White seems to have gotten a free Bc4 move.

With White's bishop already on c4, the move e5 is usually bad for Black, since it gives the Bc4 an unobstructed diagonal pointing at your king, as well as weakening your d5 square.

BTW: if you correct your diagram by removing the Bc4, then 5...e5 would be a respected line, as are 5...e6 and 5...d6.

5...d5?! looks logical enough, since the pawn is defended twice and attacked twice. But it fails for tactical reasons after 6.Bb5! The variations are a bit complicated, but it's a good example of how you have to combine general guidelines with concrete calculation

" In this case recommended move (pawn to d5), which lead to equal number of attackers and defenders on d5..."

Incorrect.  White has 3 defenders for d5, while black has 2 attackers. 

General principles are fine, but you have to look at the position in question.  1...ed4 wins  a piece.

My screenshot is from analyse board after I made my move e5 (which the engine did mot like, it preferred d5 which is indicated by the green arrow). But maybe confusing if you are not using chess.com game analyser, I make another screenshot (black to move).

Moves are:

1. e4 c5 2. Nc3 Nc6 3. Nf3 e6 4. Bc4 Nf6 5. d4 cxd4 6. Nxd4

OK that makes sense now when you mention it! But I didn't recognise this as a weakness since it is not a direct threat.

But this is probably what I need to learn, sporting and evaluating a weakness. But to be honest, I really don't know what to look for in terms of weakness /strengths. That's probably a good thing for me to do as a start, learning the basics when it comes to evaluating a positions and identify strengths, weaknesses, threats etc.. What's the best way to learn this?

6...e5 leaves a hole on d5 that can be occupied by Nd5 and a hole on d6 that can be occupied by Nb5-Nd6 and opens the attacking diagonal for Bc4.
6...d5 wins a tempo with attack on Bc4, contests the center d5/e4 and opens a diagonal for Bc8.

Thank you for posting the new diagram. Everything is a lot clearer now!

I think we've covered the drawbacks to e5: It seriously weakens the d5 square and increases the scope of the white bishop on c4. Your pawn on e6 blunts the power of that bishop.

But what about d5? While d5 "wins a tempo with attack on Bc4, contests the center d5/e4 and opens a diagonal for Bc8," there are drawbacks too! after 1...d5 2.exd5 exd5 3.Bb3 Black is left with an isolated pawn on d5, which could prove to be a weakness. Aside from that, the move looks fine.  You might also look at 1...Qc7. Sometimes you don't need to resolve the pawn structure immediately

Yes, Black seems to have a pretty decent game here.  It looks as if White met 5...e6 with 6.Bc4. That doesn't look right [Disclaimer: I'm not a Sicilian expert!]

Yeah but I'm playing 1000-ish rated people so that's mord a rule than an exception that we don't follow the main lines allready after a few moves.

6...Bb4 or 6...Qc7 are indeed better than 6...d5 7 exd5 exd5. 6...e5? 7 Ndb5 loses.