Re: How does the sink know if I am connected to a hose or using the tank?
If there is pressure in the water system and water in the tank then water will flow from the faucet at the sink. Either from city or campground water or from the water pump. City or campground water = constant pressure. Water pump, with the main switch on, has a secondary automatic pressure sensitive switch so when the pressure drops the pump then starts.
Re: I assume I don't need the water pump on if connected to a hose, but if not connected, do I need to keep the pump on the entire time, or only when I need water.
I turn the pump off when connected to city or campground water.
I also turn the pump off when not connected to city or campground water and I'm finished using water for the near future.
Turning the pump on only when needed is what I'd suggest. I'll leave mine on if I'm cooking or washing up or going to be doing dishes soon for example. But most of the time, the switch is off.