1. are backup generators constantly running, so when the lights go out to the people inside it seems like they have not?2. what do they run off?
They are not normally running. If power fails there will be some automatic emergency lighting powered by batteries which should allow the backup generators plenty of time to get started. They are often diesel powered. You can hope that they are reasonably maintained and tested from time-to-time.
Back up generators are kept as stand bye.In hospitals and other important places they take start immediately when voltage drops in the main. They Run with petrol or diesel oil or other fuels/