Actually, neither is correct.
The window to obtain a new fastpass is generally 2 hours so for example, if you get a fastpass at 1:00 and the return time is 4 hours away at 5:00, you can get a new fastpass at 3:00. So, in those situations where you have several hours to wait for your return time, you could end up with more than one fastpass.
Fastpass is not unlimited at this time. It's been posted on the board that Disney was experimenting with some fastpass rides at Epcot recently. Apparently, you could get a fastpass for certain rides there and then still get a fastpass for another ride. I'm don't know which rides this was for or if they are still doing it.
I hope this helps at least a little bit.