Why would moving to f3 be a mistake here? and why

And why would c3 be best?

Hint:

If it were black's turn, and if black played pawn to c6, then how would you save your knight?

oh i see - not a lot i could do.

And is the thought that if I had instead moved my pawn to c3, that I could at least then allow for my knight to retreat to b4, which would be protected by c3? (my knight could still be taken by black bishop but at least I could then take with my new c3 pawn, a fair trade)

Yes, and that's the reason for c3, good job

Llama didn’t you close?

There is a small magnifying glass icon at the lower left corner of the board, just below the a1 rook. If you click on it, that leads to engine analysis of the position.