chess online

Is it? Seems fairly thematic to me. The LSB is developed, the pawn can't go to e4, protection is added to d4. Maybe Nc3 usually comes first, but I don't see much wrong with the text.

It locks in the dark-square bishop. And that's 3 pawn moves in a row by white.

At the moment the d-pawn is not in need of defending. So it is logical that White keep the build up on d5 with 3. Nc3. Even though it is likely that white will play e3@ some point now is not the time. As dsfei correctly points out it hinders the development of the dsb

Unnecessary since white has nothing to fear from Bg4. In this white should focus on developing his own plans. Reacting to blacks will cost him

I think the idea behind b4 is to prevent ...c5. However, if black play ...c5 now white has the D4-d5 response. With a good game. So 7. Nc3 is stronger. An alternative for white is the slower 7. B3!? C5 8. Bb2

There is a much better ways of defending e4. Such as 10. Nfd2 e4 11. Be2 and e4 may so prove to be a target

Piece exchanges tend to benefit the player who's behind in development though? I think more clarification is needed on your comment here. And it's hard to argue either side is really ahead in development to any significant degree; black's LSB is the least-developed piece on the board, for example.

Black's light squared bishop is very well developed on c8. It is very typical in the KID for the bishop to sit on c8 waiting for the chance to give its life up on h3.

Fairly obvious resource. Black may have to ask what his queen is doing tucked away in the corner.

Black's queen is on an open file, and forms a potent battery with the bishop on the long diagonal. What more do you want?

Cdeburca the queen a8 is a monster

Don't see any real need for this at all. In addition to h3 being weak, the whole a8-h1 diagonal is weakened, and the knight on f3 is deprived of a defender. I'd be thinking about f5 and then Nf6 now for black to try take advantage.

You're taking a tempo to save a tempo though. Was there a particular line where the check was important for white?

Yep, white presumably overlooked the bishop sac, and black punished him quite well after that. I don't really agree with some of your analysis of the game up to that point though. Some points could maybe be elaborated upon.

It's not White's move, so this is not zugzwang.

Nice finish!