Is it good to sacrifice a minor piece to make the other king move before castleing?


The opponent can move their king to safety, but it will take multiple moves.
Therefore if you have active pieces in that area of the board, this kind of sacrifice can be good. You can attack before they have time.
If you do it early in the game however, when most of your pieces are not in play yet, then it's almost always very bad.

No, under normal conditions 3 material points is not worth loss of castling privilege. However 1 material point (trading a minor piece for 2 pawns) is probably pretty equal, and it's definitely worth a pawn in open positions. And as usual, if the opponent has made an error and thereby thrown off the positional equilibrium, then all bets are off, tactics prevail, and it might well be worth a minor piece, depending on the specifics.