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London System
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Just about your opening. After 5. Be2 black is fine, the KID setup with d6 and g6 is a good structure vs the London system, but from here you start with the wrong plan. The move c6 and then d5 is too slow, the pawn is better on d6, because it neutralize the Bishop on d4 and controls the important e5 square(In the london system white always want to put something on e5).
The normal plan is to make e5 work for black. The better plan was imo to play the normal KID setup with 0-0, put a Knight on Nd7 and a rook on Re8( maybe play Qc7 if needed, but not preferable) and try to push e5 at the right time. Another option might be to play delay e5, but go for a blockkade on the dark scquares and play c5, maybe b6 and try to exchnage the important Bishop on Be2 with Ba6.
Another key mistake is that you try to push your own pawns with 10. .. g5?? White loves to attack on the king side it is one of the long term ideas of the London system, put something on e5(mostly a knight), then slowly tro to setup a king attack by pushing pawns and put pressure on the king side on h7 or possible g6. With g5 you are helping him in his plan. Vs the Londong system you want to counter attack in the centre or prepare for the better end game by trading off some pieces, so he doesn't have the force to go for a mating attack and then use your own solid position to possible win in the end game.
For the rest of the game you are desperatly trying to make f5 work for your own attacki, but you shouldn't attack here on the king side vs the London, so i strongly disagree with your conclusion. My conclusion you had the wrong plan and you helped White a lot with his plan. I Looked up for some advice video's and Chessexplained on youtube has a nice serie on how to play vs the London system, it is called Fight the London System with Black. He is one of the best teachers and explains it very clear how things work. Gl 
I got killed this game, mainly because I hallucinated some kingside attack for white.