Possible Refutation to f3 in Sicilian

I was playing a blitz game and a guy played f3 instead of Nc3 to defend the e4 pawn in the sicilian.  I decided to try an aggressive approach...

I know it only happened because he played Nf5, but is what I did a good idea?

6.Nf5?! d5! is good for Black. Both 6.Nb3 and 6.Bb5+ are better moves.

But normally white does not play Nf5 to e5, normal move is Nb3. On Nf5 I think Bx f5 gives advantage for black, and you do not need a sacrifice which is not sound.

Did no one see the mate at move 16 for black instead of castling (just wondering since no one mentioned that?) Must have been cuz of the time

Did no one see that it was mentioned (just wondering since no one mentioned that?) Must have been cuz of the time

nothing wrong with f3 there, in fact it's a nice line if black doesn't know the best response.