Do I need to unplug my hot water recirculating pump when I turn off the water to the house?
Running the pump dry for an extended period can damage it. You should unplug it rather than let it run dry.

If it sits idle for longer than a couple weeks for vacation, minerals in the water could cause it to stick when put back in service. It usually just means you have to disassemble the pump and free the impeller before it will work again.

Good luck!