Jecht could get to Spira because "Dream Zanarkand" is an actual physical location somewhere in Spira. The city isn't really a dream, but a huge Aeon, all the inhabitants are also technically Aeons with their own wills. So Jecht, Tidus, etc were all physical beings in the real world, that's why it's possible for them to get from Dream Zanarkand to Spira.
As for what happened after the game ended and Tidus jumped off the ship, idunno :p.