Can a room be double-booked?
No. Each room can be sold once per night. Online, phone and walk-in bookings all share one calendar, and a booking only goes through if the room is free for every night.
If two guests try to book the last room at the same moment, one gets it and the other sees that it's no longer available.
Booking sites
Set for Stays doesn't connect to Expedia, Booking.com or other booking sites. If you also sell rooms there, block those rooms or nights in Calendar so you don't sell them twice.