Hey ThrillerFan, I really like that game, but as an 1800ish player I cannot say I fully understand why h4 needed to be played before Bh3, and what the point of Nf1 was. This is not criticism- I am wondering this because I might want to play the Adcvance myself and I want to understand it better. I know these are standard maneuvers in the Advance, but I am interested in playing the Advance and I want to know why these are played. Thanks.
The 9.h4 idea is played before 10.Bh3 for a number of reasons.
First off, castling Kingside for Black is kinda odd. Not sure why he did it. The h4 push prior to Bh3 is that often times a Knight will use h2 to go from f3 to g4. Another reason is to avoid ...g5 ideas by Black if he does castle the other way (again, more typical). It also avoids the ...h7-h5-h4-xg3 trash and Black using the open h-file to attack. All around, it just makes more sense than to block it on h2, not giving the Knights the ability to manouver, and encouranging h-pawn storms by Black.
The reason for the Nf1 move was to re-route the Knight from d2 to e3 and possibly attack f5 if a Bishop for Knight trade is made, with Black capturing with the pawn, or to be re-routed to g4 instead of the f3-Knight going there thru h2.
Yeah now that I'm thinking about it, I remember seeing a video about the Advanced French where it talked about the ...c4 line. It said that Akobian has played it a lot and that black usually castles long.