Pump cycling ON/OFF (over a short time period) when not using water means there is a leak.
Pump is an ON Demand pump..........meaning pump should only come on when system pressure drops.
So a small leak will cause pressure to drop...pump comes on/pressure comes back up/pump turns off until leak causes pressure to drop again.
There should be NO noise unless pump is actually running otherwise the pump/motor are not doing anything.
Pump running constantly & loud was probably due to low water level in fresh water tank---losing suction (when you were home)
Hum/whine could be due to a faulty check valve in water heater outlet or the one in city water inlet.