Yes, that's the point of a UPS.

It has an internal sealed lead-acid (SLA) battery and a pure sine wave inverter. All the ones I've seen use a 12-volt battery, which is charged when plugged into the mains. The batteries do not have a lot of capacity, so don't expect a long run-time.

I see no reason why a solar panel couldn't be connected to the battery to extend the run-time. And in theory (I haven't tested it), connecting to a car battery should also be possible.

The catch is that some models shut down once the battery is low, and will not restart until reconnected to the mains. I've tried restarting by plugging them into a modified sine wave inverter with no luck; maybe I need to attach an earth ground.