Why is 6. Nge2 better, and 7. d5 a necessary push in this game?

Question

I have two questions about a recent game that I played on Lichess.

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Question 1:

Why is it necessary for White to push d5 now in the game, in this position, and why is Be3 a blunder?

I did play d5 later in the game on move 10, but I cannot understand why, if no disruptive move such as c5 or a well timed e5 (although probably impossible here) is made, I should push d5 at all.

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Question 2:

Why is e2 the best position for the King's knight, and not f3 in the next diagram (on move 6 by White)?

There does not appear to be any annoying pin of the knight on f3 by a bishop on g4. Plus, I do not think it is disadvantageous to have doubled pawns on my position(if needed I could play Bd2 when Black plays Bb4). Lastly, and more importantly, the knight on f3 can jump to e5 if possible.

Answer 1

1) After 7.Be3 Bxc3 8.bxc3, Black could have won the e4-pawn with ...Nxe4. The purpose behind 7.d5 would have been to block the b7-bishop, preventing Black from winning the pawn.

2) I don't think 6.Nf3 is that much worse than 6.Nge2. Lichess still says White's better by 0.7. But the advantage of Nge2 is that it protects the c3-knight and after 6...Bb4 you can play 7.0-0 with no issues. Since now 7...Bxc3 is answered with 8.Nxc3, and you still have a knight on c3 (preventing Black from winning the e4-pawn).

Answer 2

Nf3 is not horrible (it actually transposes into a position that Kasparov once had as White, and won.) I think the reason the engine doesn't like it is that after your proposed Nf3 Bb4 Bd2, Black may play Bxc3. If that knight is on f3, than after you retake with Bxc3 or bxc3, Black can safely take on e4. If instead the knight was on d2, then you just play Nxc3 and e4 is defended. (See the blunder by Black a little later where he doesn't take on e4.) You do have other options after Nf3 to not lose the pawn, but your pawns may get doubled.