Extreme pressure on f7 at the beginning

4. ... d6 Why not d5? It's better if you respond the bishop. You can do it at turn 5 too.
6. ... h6 I don't know, but I don't like it. h5 maybe better.
7. ... c5 You can still kick the knight with Nh7
8. ... Nfd7 Why not dxe5? Your condition can be better with that.
9. ... fxe6 I agree with this move, or your opponent who eat your pawn.
11. ... hxg5 Bxd4 I think it's the best. Because his king also not protected, you can give checkmate or gain queen (with his blunder) if he don't guard his king. If he play right, you not gain checkmate or queen, but you give counter attack. With :
12. hxg6? Qa5
13.(Guarded with any) Bxf2
14. ... Nb6 It doesn't giving defense to king. Better Nf6. Also cause of that, forced mate coming
You better not afraid to having a risk with taking pawn. Passed pawn really giving pressure on game.

I had the same situation like you at my last game but I managed to make him resign in spite of his skill

It dawns on me that he might be trying to do the fishing pole so I'm not going to take the knight, but I'm not sure exactly how to defend.
Just curious: What did you calculate and rejected taking the knight? If there's a fishing pole here, then it's certain that the fish isn't you. Most probably your opponent decided shedding a piece without actually calculating anything at all, and you rejected taking it because you have calculated the same moves as your opponent.
Let's suppose that you are afraid to do so, and you want to stop the (non-existing) pressure on f7. What comes? Right on: 7...d5, when Black has a huge advantage due to white's reckless play.
I could go on, but it's pointless. Forget King's Indians and such, concentrate on classical play, and try learning and understanding the fundamentals before goind "advanced". Else, chances are you will never, ever learn how to play.