king-queen vs.king-pawn
What do you mean how do you get to f3? simple move the queen from f4 where it is currently at to f3.
Why not 4.exd3? Which direction is it anyway? 1-8 or 8-1?
Comment: A waste of time because queen checks and forks pawn and king and then king moves to support king every time.
17. Kf3! e1=Q 18. Qf2# mates faster.
I assume you mean Qg2# as Qf2 and black's queen will capture
Yes, it is. The point is that every time the black king moves in front of his pawn, white gets a free move. That's when the white king moves in for the kill. The trick is to force the move in front.
By figuring out the basic pattern of checks, forks, and pins by the white queen, you can do a 20 move calculation quite easily!
White has just queened with check, try to win