Damiano's Defense

Qe7 is best, as other moves lose instantly. I think the best move is Nf3 in the position. A trap to watch out for is Qh5? g6 Nxg6? Qxe4 forking king and knight.
3.... Qe7 is the best move for black. But this is one of the openings where I would have to ask why you would play it in the first place. What does 2... f6 accomplish? I'm not saying that it loses instantly; I just can't find any good reason to play it. You have so many developing moves like Nf6, Nc6, and d6. The only reason to play the Damiano is "because you can."
I had a friend who played the Creepy Crawly for a while (1. h3 2. a3) just so he could say he did. He correctly stated that it wasn't a bad opening because white could follow up with c4, d3, and Nf3 and turn the position into a reverse Najdorf in which Black couldn't play Bg4. However, the same idea applies. White has better options, so there is no reason for him to opt to play black in the Najdorf.
So just because an opening doesn't lose the game does not make it good.
Damiano wrote his treatise in 1512 (yes, exactly 500 years ago). This defence (which was by no means recommended by him) was one of the few openings he analysed.
Since he wrote the first extant work on modern chess, later authors felt obliged to include the Damiano Defence in their works as well. And so it passed from one generation to the next.
The Damiano Defence is of mere historic interest.