The answerer of askers is asking? Never thought I'd see the day ...
All joking aside, I'm not really sure at all, because I am not a Sicilian Najdorf Player. However, I think your question is a very good one ... so often it happens that after you've played an opening for 5+ years (in my case I've played the English since 2010) and then ... your opponent tries a new and weird move order that you've never seen. Sorry I can't help ... Najdorf is not my area of experience. 
It's a common enough approach, especially against the Velimirovic Attack. Black's pawns go as fast as possible and the knight development is delayed. It probably shouldn't work as well against Bg5/f4/Qf3 but Rxd4 Nc6 doesn't seem very convincing.
Why not 18...bxc3 19.Qxh7+,Kf8? There doesn't seem to be a way for white to exploit anything and I recall some similar positions from Soltis' New Art of Defence in Chess where the defender's king simply slips away when the attacker's pieces are left uncoordinated and even vulnerable on the back rank.
White was dreaming of a kingside attack that wasn't there and you helped his dream come true by blundering with fxg6??
16.f5? was the start of white's troubles since his pieces weren't optimally placed to exploit an ...e5 push or pressure against e6 in any way and the control over e5 was far more useful to white than the kingside space and pressure against e6.
Soltis in Pawn Structure Chess also went over the f5 strategy for white against the Sicilian and how black can deal with it. Black dealt with it correctly for the most part.
21...bxc3! 22.Qxe5,cxb2+ 23.Kxb2 and the king is more open equalizing the position. Otherwise white has active pieces and a secure king.
35.a4 there seems to be no real urgency to chase the rook. 35.Kd4 seems most logical as any valuable squares around the king are covered and space is cleared for the c-pawn to advance and white can prepare converting his passed c-pawn into a passed a-pawn, though it's generally a bad idea to exchange down when winning the a-pawn is quite far from the black king. White is still a little better after 35.a4 however but it didn't look like time to advance yet and handed black a tempo.
41...Qg1+ was the only move to hold the draw and black can keep checking the white king.
Interesting pfren, so maybe that explains why most books I've seen give ...Be7, ...Nbd7, and ...Qc7 in some order as moves 7, 8, and 9, holding off castling, at which point White has 10.Bd3 or 10.g4, and after 10.g4, Black castles.
So possibly he castled too early (Similar to castling too quickly in the KIA vs Sicilian, committing too soon) and 10.Bd3 may be the better idea than 10.g4. I'll have to look into that...thanks for the suggestion.
Why not 18...bxc3 19.Qxh7+,Kf8? There doesn't seem to be a way for white to exploit anything and I recall some similar positions from Soltis' New Art of Defence in Chess where the defender's king simply slips away when the attacker's pieces are left uncoordinated and even vulnerable on the back rank.
White was dreaming of a kingside attack that wasn't there and you helped his dream come true by blundering with fxg6??
16.f5? was the start of white's troubles since his pieces weren't optimally placed to exploit an ...e5 push or pressure against e6 in any way and the control over e5 was far more useful to white than the kingside space and pressure against e6.
Soltis in Pawn Structure Chess also went over the f5 strategy for white against the Sicilian and how black can deal with it. Black dealt with it correctly for the most part.
21...bxc3! 22.Qxe5,cxb2+ 23.Kxb2 and the king is more open equalizing the position. Otherwise white has active pieces and a secure king.
35.a4 there seems to be no real urgency to chase the rook. 35.Kd4 seems most logical as any valuable squares around the king are covered and space is cleared for the c-pawn to advance and white can prepare converting his passed c-pawn into a passed a-pawn, though it's generally a bad idea to exchange down when winning the a-pawn is quite far from the black king. White is still a little better after 35.a4 however but it didn't look like time to advance yet and handed black a tempo.
41...Qg1+ was the only move to hold the draw and black can keep checking the white king.
Based on the wording of your message, I think you may have it backwards, like you say "White was dreaming of a kingside attack that wasn't there and you helped him ...".
I am White here, not Black! (Sorry, my endgame play may not be GM level, but it's lightyears better than Black's endgame performance - I ain't THAT BAD at chess!) My g6 push was desparation, and taking the second time with the Knight is clearly better, hence why my main question was about what White should do at move 11, but pfren has pointed out that possibly the reason Black normally waits to castle until after 10.g4 is that 10.Bd3 instead could be an improvement if Black castles too soon.
Also, I haven't ran it thru a computer, but had he played 21...bxc3 22.Qxe5 cxb2+, I was heavily considering 23.Kb1 over 23.Kxb2
Played the following game last night. While I did "win" after complete and utter failure the first 20 or so moves, failure by Black to take advantage, and herendous endgame play by Black, I still have a question about it.
You will notice after Black's 10th move that Black has not developed his Knight, normally to d7, and actually, 10...Nbd7 is a direct transposition to the Classical Variation. Is there some reason that omitting this Knight move is bad, or did Black find a novelty? See below: