Coz it was destroyed in the film. But they always put it in. It's just to show off that they have one.
Nope, there are now an infinite number of Deloreans. Hell, there were two within a few miles of each other at one point in BTTF3. That was always one of my biggest gripes.
Doc gets hit by lightning and goes back to the old west.
Doc hides Delorean in cave.
In the future, Marty uses the Delorean from the cave to go and rescue Doc in the old west.
Marty rips fuel line upon getting to the old west.
Neither of them think to borrow the fuel line off the Delorean that Doc just recently hid.