2. In the end, Rufus was cured of his Geostigma, so there's a good chance he's not dead.
3. I'm pretty sure Reeve still controls Cait Sith, but probably in a secluded location. I don't know honestly.
EDIT: I actually remember seeing that scene you mentioned on Youtube,so I'm not too sure now. Probably should play the game
4. The ancients were killed by Jenova. They explained this through Gast's video logs back at Icicle Inn: Jenova came from space and appeared as a friend to the ancients, but then started a disease that spread among the ancients and turn almost all of them into monsters.
5. I'm pretty sure the Turks still exist. Rufus is still around so he may continue to need thier services.