Review of recent online encounter

I don't normally play 1 g3, but it is a fine opening move.  Where I go differently is after Black's 1...g5.  Consider an immediate 2 d4 or e4.

Through your first 7 moves, I would not double fianchetto my bishopes.  Again, I would want to gain central space with my center pawns, instead.  And because of Black's kingside weakness, I might not castle kingside so quickly in order to keep the possibility of h4 to meet Black's g5.  Luckily, Black is daydreaming through the opening...

When you ask if there's a faster way to checkmate, I think you mean after 24...Kxc7?  You may want to simply consult a chess engine for that. 

But I play 25 Qf3 instead of Qe2...  It coordinates my Q with my B and makes them an attacking pair. 

What would e4 have gained me in the starting moves?

I see the point about central space, and have seen many great games with the use of central space. I did see the kingside weakness, but as soon as I Fianchettoed my second bishop, I had the option of going up the Queenside whilst using a rook to protect my Queen. 

e4 would open up your queen's diagonal to the critical h5 square.  You may not have an attack right away, but threatening it can help to create weaknesses.

e4 would also prevent Black from winning the center, which a thinking opponent would have tried to do versus white's mechanical development.

You should never consider play on the flank unless your opponent's breakthrough in the center is impossible.

Try your double fianchetto opening against a computer and see what happens.

Did whit castle at the right time? I did capture black's rook with my knight that was part of my defence, but succeding that the a file was opened up.

I see the H5 square attack now.  

 My point, exactly.

I can say that black should have gone with 1... e5

I don't know.  When I rockclimb, I "downclimb", or sort of climb down and notice all the foot/hand holds I missed.  Although I made it to the top, I see all the potential holds that might've made the climb easier.  Although I agree reviewing a loss is a good idea, reviewing a win isn't necessarily a bad idea either, as you can look for tactical plays you missed.  I've won games (in blitz atleast) where I won a piece, lost a piece, and then won after a closely contested endgame.  I think these games are important to review as well.

As for the game, black's play was goofy, for lack of a better word.

I once showed a blitz game, a muzio, to a friend of mine, a particularly astute player, in which I had devastated my opponent in, I don't know, 2 dozen moves or so. The reason was to demonstrate the power of a certain line I had adopted at the time. He looked over my game and said it was wonderful (awwww...) and the only criticism he could think of was where I had missed mate in two on move 13. .. well... duh...

He told me the lesson to be learned was simply to never analyze blitz games.

A corollary might be, never analyze a game where your opponent played poorly.

There are reasons for showing a won game. One is because you're proud of it and want to show it off.. as good a reason as any. Another reason is to verify that the problems you posed to your opponent, that he failed to solve and thereby lost, were indeed irrefutable... that your moves (or plan) were solid and not just apparitions made to seem solid through your opponent's mistakes. In this, you learn something and grow. Once you do opt to show a game you won, for whatever reason, you've opened yourself to critical analysis and must accept it without justifying or explaining - the move list tells the reviewer everything he need to know. It's sharky waters out there, I know.

Йоу