Is castling really all that important?

Don't look like it in this game I played as white.

Most of the time, castling is pretty good. But there are certainly times where other things take priority (for example, maybe you find it worth winning material at the cost of being able to castle). In this case, black's pieces were cramped and had a hard time getting to you, so, since you were winning that important d5 pawn, it was probably worth giving up castling rights. Usually when the game is more open you don't want your king to be a liability, which will distract you from connecting the rooks and coordinating all of your pieces.

Another way to put it: When you're in control, usually a slightly exposed king will be hard for the opponent to exploit; if you're under pressure, then an open king will make it all the more easy for him to hurt you.

Castling is overrated.

I highly recommend the book From the Opening to the Endgame by Mednis as a supplement to your recent chess experience. :)

In those lines of the French where White pushes all those pawns, it's sometimes okay for White not to castle. In general, you really can't overvalue castling.

This might be slightly off-topic, but in crazyhouse castling is pointless.  The king is just as exposed (or maybe more because in the corner it has less escape sqaures), so there is no point in wasting the move by castling.

Very well coordinated counter attack by White in the opening. I also was impressed by how Black managed to castle and then get the rook there in time. I'll have to study the opening further to see where White's flaw was. I don't know if Black could have lead a better attack or prevented getting tied up by the counter attack.

As for the middle game:

21. ... Black should not trade when already down material, which leads to a losing endgame. Instead, Black should have exploited the bishop pinned to the queen and  played: 21. ... a6 (keeping the queen off b5 and opening a7 for the rook) followed by 22. ... Ra7 and 23. ... Bxd7, restoring material balance.

The next move that really struck me was 28. ... Qh1:

This is not exactly pawn grabbing since it is aimed at the king and hopes of perpetual check in a lost position, but it fails and the queen probably should have stayed in the center. Fortunately White got worried and played 31. Kf2, however White should have played 31. Qf7 (31. ... h6 32. Qxf7+, 31. ... Be6 32. Qe8+, 31. ... Qxg2+ 32. Ke3 and Black runs out of checks and can't return in time to save the bishop)

I stopped there.

Castle early, and often.

That is backwards. It should be from the Endgame to the opening. You have to know which endgames can be won before you choose them in the middle game, and which middle games can be won before you choose them in the opening. Or you can just take your teacher on blind faith until you learn the endgame at the end and it all finally clicks.

Backwards? Have you read the book? It introduces several lines in which queens can be traded and castling skipped with an advantage in the endgame thereby illustrating which lines lead to favorable endgames. Btw, one of the best ways to practice good endgame strategy is to get there in the first place. With respect. :)

This is how I would have  played if my opponent went with 31... h6 as you suggested

Yes

O_O

You misquoted me. I did not suggest Black play that. I suggested that White play 31. Qf7.