Continuity check....

Nothing runs on continuity. I would test for voltage on the affected circuits with the load device powered up. I am not real clear on what you are testing where and how. Are the well pump and water heater running on 120 volts or 240 volts?

You should have two power feeds and one neutral coming into the main breaker box. Start by ensuring you have the proper power between each leg of the power feed to the neutral. The neutral is the return circuit to the generating plant so it is just as important as the power leg. Work your way down each circuit to the load device while checking voltage, one step at a time.

If the voltage loss is the same at the water heater in the house as it is at the well house, that would lead one to believe the fault lies in the house.