All this is well-known. It is also well-known that after 6. Bc4+, Black should play the more stubborn 6... d5 covering f5 square. White then has to find or to know two precise moves in order to win after 7. Bxd5+ Kg6, namely 8. h4! h6 9. Bxb7!.
King's Pawn Opening: Damiano Defence 2...f6 is not a good move!!

Damiano didn't recommend this defense. In fact, he said it was the worst of all against 1.e4 e5 2.Nf3.
I have myself a question: what about 3...Qe7 after 3.Nxe5? Should white play 4.d4 or 4.Nf3? I believe the e5 knight is now seriously threatened by the f6 pawn.
e4 e5 Nf3 f6 is very weak, white can take on e5 which is better for him, or he can play d4 which also gives white a better position. No point in f6 on move 2, a move that does not do anything and weakens the diagonal toward the king.
I thought 3. ...Qe7 might work as a gimmick, Chigorin even played it. However it just doesn't work, there are no real positives for black, he is just bad. In Chigorin's game he lost his queen early on but still played well - he then missed a mate in six starting with move 24 and again on move 25 in this remarkable game:

3...Qe7 is a different move, and loses differently.
You made a nice board for me to discover!

Damiano didn't recommend this defense. In fact, he said it was the worst of all against 1.e4 e5 2.Nf3.
I have myself a question: what about 3...Qe7 after 3.Nxe5? Should white play 4.d4 or 4.Nf3? I believe the e5 knight is now seriously threatened by the f6 pawn.
Thanks, but 3...Qe7 just a defend move, so 3.Ne5! is a best move for White.
If 3...g6 White will 4.He5+, Please comment if you have idea to play after 4.Hh5+. Thanks