Queen's pawn game theory questions?

I was wondering who is better in this position, black is a pawn down but what is his compensation and why is it considered compensation? Is it worth a pawn and what will it be used for?

Also I've always wondered why is it considered bad to block the c pawn by playing nc6/nc3 in queen's pawn games? Everyone keeps telling me its a inaccuracy to do so since the c pawn is best used to contest the center or reinforce it via c3/c6 or c4/c5 but what about the f pawn, why is it ok to block the f pawn and not the c pawn, the chigorin defence also seems to "violate" this theme. One last question is how would you handle these (diagram below) type of positions? I would appreciate the evaluation of it on who is better or the pros and cons of both sides. 

I'm hardly a very strong chess player but Jeremy, I hope that these diagrams don't represent what you commonly see in your games as White. I'm left cringing at the way White has played all of these positions.

Diagram one: I don't know what you're talking about at all here. White is not a pawn up and has played outright horribly this whole line. Every single move apart from 1.d4 is a bad move. If you play like this as White regularly I'm not sure how you haven't worked out yet that you can't hold onto that pawn.

Why shouldn't you block the c pawn with a Knight but the f file is OK? So that you can play like Black did in D1, not White! It's too much for me to explain... Also, why would you want to able to move your f pawn?!? I just can't comprehend. You badly need to stop playing Queen's pawn openings if this is your understanding of them.

Diagram two: This is a strange move by White. I don't really like it. Black's Bishop is somewhat akward there. By simply playing Nf3 White is forcing Black to make a small compromise in regards to that Bishop at some point. The most common of which would be playing h6 or allowing it to be traded off for White's Knight.

That said, White is better here. More space. Much more space. If a database tells you otherwise that will be because this position will more often than not be reached by White players who don't play these positions well, hence the last move. White is still better.

Diagram three: Still with the White player not even trying to play for an advantage... I don't know that it particularly matters how that Bishop tension is resolved. The position looks very equal after a whole bunch of possible next moves to me. Again here it looks like Black is going to be playing c5 with a nice position.

I would be delighted to have any of these positions from the Black side.

Diagram one looks like a reversed QGA. Looks playable, but the bishop on e2 might not have been best move...I'd say "with play for both sides"

Diagram two is usually frowned upon from the white perspective because white is giving up his bishop of opposite colour to his pawn chain. I disagree because I believe white's space edge makes up for it. I have several successful games with this. From the black perspective there is a famous Nimzowitsch V Capablanca game where the latter wins and is touted somewhat as the lines "refutation".

Diagram three is a good equalising try by black.

In the first case, White has voluntarily given up his most important central pawn and is playing a Queen's gambit accepted where he is trying to hold the gambit pawn. White may be able to get away with this, but it certainly doesn't work out for Black when white plays a standard Queen's Gambit. In the 2nd diagram, White is giving up one of his best attacking pieces, the Kings Bishop, for the problem piece of Black in QP openings. In the third, White can play Ne5 which I believe is what most London system players would do. This is not so bad, if you are in to that type of opening. You should study the actual Queen's Gambit and see how White  uses his C pawn to pressure the center. That is the main line for a reason, if you don't do it you are playing Black with the White pieces.

I'm not sure why I didn't mention the "good Bishop" idea. I probably thought it went without saying that trading a Knight for Black's Bishop was better because White wanted to keep his "good Bishop". Anyway, I don't agree that Black can force an endgame here at all. You're telling me that White isn't better here? Looks better to me.

I'd rather be black in the first position.

As for the Caro line you gave, there exist lines where white gains something from trading LSBs in the Advance but doing so right away (on move 4) is not one of them.

The line in the post above, though, is interesting, since my engine is for some reason giving white a considerable advantage. Probably it's nothing, but I guess it's a try.

Is that how you see this? Maybe you think you are a leading theorist (being the only person here with whom I have disagreed to this point) or maybe you know what the actual leading theorists think but despite having failed to mention that, assumed that I simply knew it to be true anyway? Which is it genius?

You're kidding, right? I don't even want to imagine how hard something like this specific up to date theory would be to look up!

Also, if you think that I'm the one who's been a "jerk" here then maybe you need to go back and read what's been said.

White trading light squared bishops early in the Caro is a known strategic error, there's no reason to give up your best piece so soon..

I agree that playing 4bd3 isn't that promising for white, see mentioned Capablanca games. Playing 4h4 h5 first can make a difference because after 5Bd3 BxB 6QxB e6 white can play Bg5.

When looking around databases found suprising number of FIDE 2700+ games in position with h4 h5 included. For example, recent Adams game at Tata

http://www.chessgames.com/perl/chessgame?gid=1813600

Don't really understand why would make a big difference to evalution, and yet Adams doesn't typically play positionally unsound lines.

Umm, ok I did wonder about that.