I've been seeing much of the mate in 4. I was interested in what are some of the best or better responses to this sequence for black.

1.e4, ___

2.Bc4,___

3.Qf3,___(Although in most cases Nf6 will occur here)

Also, you may have seen Nf3 in order to push the knight up to f5 in order to check black's king after castling to gain the rook (even though at the end of the exchange the point values are equal 6-6 knight and bishop for pawn and rook).

You answered your first question. As for your second question, the exchange of K+B for R+P on f7/f2 is usually bad for the side giving up the K+B because it gives two useful pieces for one inactive piece. Also, with all the other pawns still remaining on the board, the rooks won't be nearly as effective. Finally, it also tends to give the opponent a lead in development.

You didn't really get what I'm asking. I know how to preven mate in 4 by at any time before and by the third turn black will need to do ...Nf6. But what openings are there that wont require that, either because the f pawn is pushed up before hand or that the f7 square is well protected. It goes the same way for the N + B for P + R. So I'm interested in openings that will prevent mate in 4 and ones that while trap whites pieces when they attempt it as well as preventing and traping white when he attemps to do the N + B exchange for P + R.

ummm, ...Nf6 is the ultimate answer to the Scholar's Mate. If you want to know openings where Black doesn't bring his knight to f6, then you are asking for openings where White usually develops his bishop to somewhere other than the a2-g8 diagonal. Oh, and if White actually tries to go Ng5-xf7 and trades the B+N for R+P, then he's basically trapping himself!