My gym charges extra for ICE (a competitor of Spinning®). You can sign up for an 8-week program, I think it's two or three classes a week, which guarantees you a slot, otherwise it's first come-first served.
It probably varies a lot by gym.
I don't spin (I need shorter crankarms, the one thing on those bikes that isn't adjustable), so not much help here - but depending on the gym, the bikes and the amount of time between classes, you may be able to bring your own pedals and saddle/seatpost. Some gyms have SPD pedals on their bikes, so if that's what you use you could wear your own shoes.
Definitely shop around.
Speed comes from what you put behind you. - Judi Ketteler