Questions on power stations and water supply

In an apocalyptic world where people working in power stations and water treatment have fled-

1. How long before buildings would no longer receive electricity? Basically, how long can power stations generate and supply electricity for with no one to control and regulate it for?

2. Same as above but in the context of water supply

3. How long would a back up generator in a supermarket or hospital generally last for once it has been activated indefinitely?

Thanks, that pretty much answers everything and more