OK I will give this a try. I can’t see the well. I assume it is a well point, driven into the ground 10’ to 15’. Also assuming there is a check valve on the suction side of the pump. What I can see us a jet pump, an inline filter, water softener, and about an 80 gallon standard hydro tank.
The pressure switch on the side of the motor probably needs to be replaced. That is the thing with the plastic cover and points that snap back, probably a 30/50 switch. That maybe all you need to get the pump to come on when needed.
I don’t know much about the filter or softener. You should duplicate this thread over in the water softener forum.