Ecologically more sound, I think it could take bath water or washing machine water depending on the kinds of soap you use, but I've never tried that.
It's best to have it operate at night, people in the garden are less likely to get wet and the water does not evaporate as quickly, so it soaks in better. You may have to adjust to your cat's nocturnal habits.
There are float switches that will disable the pump if the water gets low, but they generally need a 12volt relay as they cannot handle the current that the pump needs.
The tank will be siphoned dry if you don't have a sprinkler nozzle above the tank water line.
You will need a submerged filter of some kind, or the nozzles will block up.