What should White have done to avoid this very very awkward position?

My questions...

1. How should white have played to avoid this very awkward situation?

2. In the variation i thought up... what should white play after 3.. h6

You already answered your question with your very first game comment.  Nxh7 was uncalled for when you have viable options playing something safer with your attacked c3 knight.

I'm definitely not a strong player, but even I would have spent time analyzing the moves Ne4, Nd2, even Nb5, Nb1, Na2, Na4 or for that matter looked into exd4 to see how dangerous White's B+N combination can be on my weak diagonal.   And then .. *takes a deep breath* assuming nothing works, would see if sacrificing my Knight is a better alternative.  I think after d4, black is doing better but I'd play Nd1 (or maybe Na4) to deal with the dangerous bishop.

Did you analyze all alternatives and could you argue in a room full of Grandmasters that Nxh7 was "the" best move to be played?  I highly doubt it.  

Serious chess expects nothing but the best moves from your opponent and when you sacrifice, you have to ANALYZE/CALCULATE IT OUT.  You have to prove that even with best play, your forcing tactical idea WORKS!  Failure to do is just silly.

Desperado sacs and counterplay moves are used as a last resort (assuming all other options fail) OR if you have a forcing tactical shot ... in your case,  you seem to be lashing out without any sound justification beyond this fanciful "Oh, if he makes a mistake like g6, I will mate him with my Q+N on h7, if he doesn't, maybe I've got something else ... I don't know but I'll think of something" thought process.

Also, in the rest of your game, you miss basic tactical shots repeatedly ... exd2 being the most scary mistake of them all.

To answer your 2nd question : After 3...h6, you have no more pieces to join in on this attack that you've put so much stock into.

While it looks interesting, Nxf7 Qd7 and Nxh6+ gxh6 followed by Qg6+ leads to Qg7 and after Black plays Kh8 tucking his king to safety, you have lost way too much in material without a forcing tactical shot. Resigning seems like the idea.

2. exd4 looks like a good idea. Okay, he can recapture with check. Whatevs. There's simply nothing there indicating that Nxh7 could conceivably work.

Indeed, or why not Qxd5?

Because the d5 pawn is protected by three black pieces.... and i dont think white would be much better off losing a queen to capture a pawn...

 ...Qxd5 in the 2.Nd5 variation. 2.Nd5 Qxd5.