I think 11. ...Qe7 is more common because of white's idea of Rd1 figthing for control of the d-file.

The rule of castling applies here. Only castle when all your pieces are safe from attack. Here because black castled white has gained an important tempo and influence on a key file. The momentum is really starting to swing in White's favor.

Kavalev seems a strong player (!), so it's maybe worth looking at why he played Be8. Was it to play a subsequent ... f5 with tempo, and redevelop the bishop either to f7 (where it protects the pawn, and where it may control a decent diagonal after e5)?

My idea behind 13. ...Be8 would be ..f6 followed by ...Bg6 and black has a great bishop and flexiable centre.

now white is in the game with the threat of c4-c5

c4-c5 just loses a pawn at the moment.

This retreat square wouldn't be open to him with the bishop on e8 (though granted, you used that tempo to put the rook on d8)

I really do not like this move because the bishop is not doing much good here. 16. ...Be8 is clearly better.

i like Be8 best

I think the problem with ...Bc8 is that it takes too long for the bishop to perform any kind of active role. With ...Be the bishop will assist with control over the central light squares. Not to mention Bc8 allows a recapture of c6 if white ever trades.

I did think long and hard about which retreat of the Bd7 to play. I had visions of the Bc8 either going to b7, or, if I can get in e6-e5-e4 maybe to e6. I put this position on a search engine, which also prefers Be8

Be8 has a good open look to h8.

your pawns are overextended.

A search engine reveals Ne5 is superior to h6, meeting Bg5?? with Ne5xNf3 check followed by Qe7xBg5

A weakness is only a weakness if it can be exploited. White can't really exploit the weaknesses in black's pawn formation, meanwhile my pawns, after my b pawn captures on c6 and advances to c5, control some useful central squares.

This is why 16. ...Bc8 is bad. Now you are forced to create a major weakness in your pawns. Had played 16. ...Be8 white could not capture on c6. I understand the "a weakness if it can be exploited" comment. Despite the fact that the c pawn is not in immedaite danger it will be an easy target in the endgame. A more critical pile up of small advantages i.e the weakening of d4 and e5, the trade between a poor bishop for a great knight and the broken pawn structure. All of these combined spell rough times ahead for black.

Accepting such a pawn formation has both advantages and disadvantages, I would hazard a guess that black would want to avoid too many exchanges and try making dynamic use of the added central control the pawn gives you

!! right on the money

Actually it is not clear that e5, 20. c5 does win for white. Black does have both bishop and queen lined up against c5.

?? Here white should have gone for the exchange 20. Ne5! and there is no good way for black to defend.

I would guess he wanted to have rooks on both the d&e files however Ne5 is clearly better.

A search engine I ran through this position with, suggested 20. Rd2 as the best move here. It also suggest 20. Ne5 can be met by Bb7