How to continue (black)

my opinion:

after whites 5. Qe2, black must have played 5...Qe7 to avoid the pin of the knight and steering into an equal game.

after blacks bad move 5....d5 the position is already lost.
its whites move and white could simply play 7.dxe4 winning a piece.

Well said. So it is not acurrate at all ;)

BTW is 1. e4 e5 2. Nf3 Nf63. Nxe5 d6 4. Nf3 Nxe45. Qe2 Qe7 6. d3 Nf6

main line for black response, or are there other better responses as black?

the black knight on Ne4 has to move; otherwise its lost.
there are two squares: Nf6 and Nc5.
i would play the natural move 6....Nf6
but probably 6...Nc5 is also possible; dont know.

as white i would play 7.Bg5 or 7.d4 against blacks 6....Nc5
but black could answer with 7...Na4

Na4 looks maybe not so ideal; but the threat of Nb2 is somehow annoying.

but i have played other openings in the past and dont have much experience in the petrov. and never have seen 6....Nc5

just my thoughts.

here is a game, i have played.
i was black and somehow there was a position, where white plays Nc4 instead of Nf3.
of course its not the same theme and a different position. but also there white puts the attacked knight on the c-file instead back to the 'natural'-square Nf3