adaption by closing the long diagonal and formation a short center

The bishop offers some psychological pressure to the queen and entices a weakening of the castle by 8.h3, both of which seem to be a plus.

against a fiancheto and knight on f3, it doesn't seem that dangerous for white

This exchange does prevent a loss of tempo or a cramped position. As a preference, I tend to hesitate to exchange bishop for knight without receiving a good benefit if possible, like an attacking initiative, because it really helps in the endgame. The only safe square for the bishop would have been c8 (temporary contra-development) or d2 (blocks the queen). 8...Bf4 would eventually be attacked by e4.

I ended up subscribing to the flank opening section on chesspublishing.com and this exchange was a large part of the June newsletter. It focused on how black, or white should the case be reversed, can find himself in trouble on the light squares without playing poorly. One thing is chesspublishing is addicting largely because of the quality of their annotation presentation. Clicking on a subvariation actually allows chess readers to step through the position on the board and snaps back to the played position when the variation ends. Once you see that kind of web presentation, you want it for your annotations!

This is GK lack of improving and evolving. I like GK and I support it in spirit and some money, but it must be said that improvements are slow. The web is moving too fast and, even if GK is very good, more things are coming out out there.

Actually these days something as good can be found on GK. Whether available or not in the notes section, you can in the comments - at least you can post additional diagrams there.

Thanks for the explanations, now I see the point of black's 7 move.

This move does take a N at the expense of the LSB. I think White gets the best in this exchange.

Is this because you are trying to avoid a queen exchange?

9...Nbd7 would indeed avoid the Q exchange, but I wasn't too concerned about that. The central advance ...e5 is thematic, and if White takes on e5 it would be nice to retake with the knight, given the position of White LSB. I didn't really think White would exchange after 9...e5, as Black's rook would be quite well placed on the open d-file. It is a playable line, though...

The previously mentioned site thought e5 too weakening given the LSB-knight exchange.

Perhaps with the idea of making the g7 bishop bad, but creating a bad bishop for white as well. The idea would be complete with e2-e4. Not the best plan for white considering 2 bishops which need lines to operate.

Closing off might not make the bishop permanently bad but it does create some difficulties for white to take advantage of his LS advantage.

Wasn't 10. e3 playable as well ?

10. e3 is playable but it undermines the pawn structure just a little and it will be overprotecting square d4 that has no real threads in the near future

When moving a pawn you need to have a plan. Would developing Bc1 been playable?

Locking the center should benefit the knights some.

12.e4 forms a Benoni-type pawn formation, which I only like as White. But then, that's only my opinion...

The bishop white move goes for Ne4. e4 is kind of bad, in my opinion, as it creates a pawn to be defended by white, and takes a good knight's square. Isn't it?

You were probably subliminally thinking of opening a line for your bishop, but the overextended pawn is vulnerable.

Advancing a pawn always "seems like a good idea at the time". But if it's quasi-isolated like this one this might prove premature.

Black is essentially offering it... nor the b2 pawn will be a compensation, since Rb1 and then Rxb7...

Are the two ideas mutually exclusive? After Kh7, Nxe4 still seems viable. The pawn cannot "run" and Kh7 denied it reinforcements.

No, you are right: the two are not mutually exclusive. Although there is a considerable fight going on around the e-pawn, White could have taken it at any time. However, Black does have chances of counterplay (e.g. against the b2-square) if White takes early. Hence, I suspect, the delay. I certainly felt during the game that my options were getting narrower and narrower the longer White delayed the capture. And, of course, Black was trying to obtain any kind of piece activity and/or counter threats to balance the loss of the central pawn.

I also had a recent experience where white played his Queen along the b1-h7 diagonal pinning the pawn. Eventually the pin failed and his position collapsed (I threatened a queen exchange and he complied-- he could have declined the exchange and maintained the pin!), but I'm convinced that under the right circumstances the idea would be very painful for black.

IMO, yes, it is. I've seen a lot of sac on this kind of black's positions - with some preparation, of course!