Tidus is a 'dream' of the Fate. As was his father, they're dreams that the fate have of old Zanarkand. When you destroy Sin from the inside you in essence let the 'Fate' stop dreaming to keep giving Aeons to the Summoners.
They gave their souls for a way to defeat Sin, and until Sin is gone permentally they can't die. When they 'die' Tidus being a figment of their dreams 'disappears.'
Yes, he did.
He was in Zanarkand when Sin first attacked, and then Auron helped Tidus get to the future Spira by basically riding on Sin, who transported them.