What you did is fine. But to take an agressive stance against this opening black can play 1. e5. The gambit is actually pretty good for black, which is why then white normally plays 2. e4 transposing back into the King's gambit(you can decline the gambit though). The good thing about the move order though is that often people who play 1. f4 are looking for a positional, not tactical game. So by immediatly gambiting a pawn, you are forcing white into being up a pawn in a tactical position or being down a pawn in a tactical position.

I really don't see the point behind 3.h3

Well said! I often use this strategy with higher ranked players in blitz just because even though they are stronger than me in strategy they can still fall into this trap. This isn't to say I don't make the same mistake either.

White's position is now in shambles.

The rooks can't be connected until the bishop moves. Dynamically White is down a rook & bishop.

Rofl. Who says chess can't be funny?

White's Bishop is like a big pawn in the position,so necessarily Black is up a pawn or two.