Some fans are triggered by a humidistat, if this is on one, it's possible the high humidity has closed the circuit. But a humidistat in a powder room isn't the most logical location for an installation. You could try localizing the circuit that it's powered from by turning off the breakers in the main service panel one-by-one. IF the fan turns off when power is removed from that bathroom, if you're comfortable, you could also remove the bathroom switch face plate and see if it's simply hot wired, or shorted. This is a basic bathroom ventilation fan and not an air exchange fan or a heat recovery ventilator, etc? Again, a powder room would not be a logical location for ether of those. If you;re not certain, you could pull the grill off the fan and see if there is a manufacturer and model #. Then there is also the phone call to the previous owner asking what the deal is with the fan.

Get rid of the floodsafe hose they are junk! They shut off regularly without valid reason. The hose they are protecting is likely to never break and they have a weak joint just prior to the floodsafe that if highly likely to failand there is no protection there.

Smack the jandy box about 1/3 of the way up from the bottom with your fist. If the pump stops, the relay needs to be replaced. If it doesn't stop smack it harder. If it doesn't stop then, you might need a new control board.

$1700 - insane. I can get the entire furnace $700. X13 You should have two speed taps for heat and cool, common 24v and the usual Black and White GRN to power the motor. X13 is ECM an motor.