Ruy Lopez opening position puzzle

I was studying moves in a game and came upon this option 7. Nxe5.  My first reaction was why didn't black play NxN with a wonderful trade.  Would you take the Knight?  If not, why not?

If you choose another move what would it be?

If you were white and black did play NxN, what move would you play?

To see the move options go to http://www.masterchessgames.com/index.php?main=Chess-Openings-Explorer&movenum=14&pieces=e4,e5,Nf3,Nc6,Bb5,a6,Ba4,Nf6,O-O,b5,Bb3,Bc5,Nxe5,