General move evaluation

@1

"computer suggests 13. Qa3 here with +6 for white. And my move has only +3"
++ That means both moves are winning and one is no better than the other.

"seriously wrong in evaluating the position"
++ There are only 3 objective evaluations: won / drawn / lost. If you are wrong between those, i.e. head for a position you think is won, but in reality is lost, then you lose the game.

"then how he improves?" ++ By analysing the lost game.

"Is there any kind of popular method of getting a good understanding of what's going on?"
Dorfman gives a degressive scale:

1. King Safety
2. Material
3. Position after queen exchange
4. Pawn structure

>That means both moves are winning and one is no better than the other.
Are you sure that this is true? I always assumed that the evaluation of position by computer is intended to be equal to the amount of pawns that one player is ahead of other. So +3 means "3 pawns ahead", +6 means "6 pawns ahead". Am I wrong about that?

@3

"That means both moves are winning and one is no better than the other." ++ Yes.

"Are you sure that this is true?" ++ Yes.

"So +3 means "3 pawns ahead"" ++ Yes, well equivalent of 3 pawns ahead.

"Am I wrong about that?" ++ No, you are right, but +3 or +6 are the same: white is winning.
A win is a win. There are no bonus points for a faster win, or for a win with more material.
The computer selects the move that maximises its evaluation, that is how its algorithm works.
For a human it is often practical to simplify a +6 position to a +3 position,
so as to get a clearer win, with less risk of messing it up.

Both are winning (I think that basically everything around +2 or more is winning, with some exceptions as engines are not perfect), though sometimes the path to the victory is far from clear. Therefore, it is good to understand why is this position winning and the difference between Qa3 and Bd6.

This is exactly why I would analyze every game and not just lost games. Here you threw the advantage after all, at a certain point, so it is not bad to try to understand why.
Look at the position after 12. ...Qb6. What do you see?

I see that white is ahead in development, so his pieces are more active, plus his king is castled, and black king is in the center. On top of it, white has more space because of central control. All of that means that black would like to exchange pieces to relieve the pressure.

Qa3 does a few things. It doesn't allow castling, so in that sense it is equal to Bd6, but it is superior in other ways. First, it doesn't allow black to trade queens, which is something he would like to do here as I mentioned. Second, it kind of exposes black's queen because white will probably have Rb1 tempo move as a threat and then he might even win b pawn, all the while improving his pieces.

So basically, queen exchange relieves some pressure from black, as this is not a position where the advantage is of a material type. Here the advantage is time, and if white exchange pieces, and wastes time, black can perhaps equalize or at least make the game complicated.

So, as you can see, this is a pretty instructive position to evaluate after 12. ...Qb6. At least, that is my opinion.

What about the move 12.Ba3?

I liked the move Ba3 instead of Bf4.

What was your thinking with Bf4?

I actually like Ba3 idea as well, in a sense that it feels right to immediately disable castling. It is kind of a natural human looking move.

On the other hand, attacking a queen with tempo is logical as well, he just needed to move his queen out of the way afterwards.

Engine evaluation depends on which engine you're using (like Stockfish version, Lite or not) and depth. There can be a significant difference between the valuation shown in the game review and the evaluation shown given when analyzing both moves Bd6 and Qa3 separately. I think the difference is around 1.6 to 1.9 which won't feel as much like you just lost a piece.

The game review is more useful for tactical mistakes than positional mistakes. With a tactical mistake, you'll see what you did wrong immediately. For positional mistakes, the game review is just the starting point for further investigation. But even then it can be difficult to see why. Besides, many positional mistakes are practically undetectable if you're only using an engine. That's why feedback from a coach or from stronger players is often a better way to improve positional understanding.