first disconnect all electrical supply to pump and then detach the pipe or pipefittings joined with pump's outlet and inlet.
A sump pump is submerged in a pit. It keeps house from flooding. A utiliity pump is used to pump water out of already flooded house, boat, pool, tank, etc....
Sounds like you have a bad zone valve or zone pump. There is either a pump, and the zones in the house have zone valves, or each zone has it own pump. Zone valves go bad all the time, you can just replace the motor on it instead of sweating the new valve in. The box that is on top of the valve.
I do not know your situation but a good guess is that your well pump is always on and is not getting enough pressure to shut off the pressure switch. So I would shut off the power to your well pump and see if the buzzing stops and if it does then I would replace your well pump. If the buzzing don't stop with pump shut off then it could still be your well pump check valve slowly leaking threw but I think its your pump because its not pumping enough to shut off with or with out a bad check valve.
A foot valve, in relation to a water well, is a check valve at he bottom of a well to keep the water from running back into the well from the pump when the pump is not running. If the check valve does not hold the water the pump will lose it's prime and will not pump water.
You switch off the pump, drain the pressure tank, then remove old gauge and fit new one.
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