No that is fool´s mate.
What's the problem with moving the f pawn?

The main problem with moving the f-pawn before castling is that it opens up a diagonal attack on the King which is difficult to block. Fool's Mate is just the most obvious realisation of that threat.

I just played a game with a newbie who pushed the f pawn, totally devastating him with my memorized checkmate combination. He did't have time to blink. Then in a rematch, he played the scotch, I blew it and resigned. I am not that good, but just memorized how to obliterate the opponent responding with ...2f6. He was surprised I didn't play with the same strength, probably having no idea f6 specifically is some sort of blunder. I bet he is playing it again without shame.

Moving the F pawn in the opening isn't necessarily bad. It just has to be done correctly or it'll be lights out. The problem is that moving the F pawn exposes the king to checks along the H file with the opponent's queen. If the G pawn is moved, it's immediate mate with Qh4# for example. There are openings, many good ones that involve using the F pawn. The King's gambit (Not played at Gm level really but perfectly viable here) and the Four pawns attack. Both are solid openings.
Anyway, the simple answer to your question is, it exposes your king to the diagonal check on the H file from your opponent's queen. If you do move the F pawn, ensure you develop your kingside knight right after to avoid that check.
I mostly move the f pawn after casiling (how do u spell that). Is there any dangers to moving your f pawn after casiling.
I like to get it gone after castling, opens the rook file
Nothing happens after moving the f-pawn because you play newbies who suck. Then they cannot capitalize on the weakness. But generally speaking, it is a huge weakness and should be avoided. But these patzers make the impression your doing just fine as they don't sac the knight on second move and then the Q doesn't wreak havoc to your king obviously.