Waterco aqua mite turned on pump but humming noise and no pumping plus pump is very hoy

SOURCE: hot tub pump will not

This can be one of three issues.
1.  Starting capacitor as you have suggested.  You can take the capacitor to a motor shop and have it tested or test it yourself if you have a meter that will check capacitance. 2.  Low/High voltage.  If the voltage is not at the proper levels (10% up or down) then the unit may have a hard time starting. 3.  Something might be binding up the impeller.  Disconnect the power and carefully check to see if the shaft of the motor spins freely. 4.  A short in the windings.  If none of these seem to be the problem, then you will probably need to replace the motor.

SOURCE: The Pump is humming but not pumping.

maybe there is an air bubble in the pump try to force water through to get the air out

SOURCE: The pump motor hums, but won't start.

A humming motor usually means a bad starting capacitor, but it could be some other things. If you see some water movement that means that your impeller is spinning and the capacitor is good, and in this case you would want to check for air leaks on the suction side of the pump. Make sure that there is water at least 3/4 of the way up in the pump and the valves are in the right position (sometimes turning the skimmer off and just sucking from the main drain can help). Also check to make sure that there is water in the skimmer, and it is not getting sucked dry. Next lubricate the pump lid gasket, and try some silicone around the threaded pipe on the front of the pump. If all this fails you could have some debris stuck in the impeller.

SOURCE: my hayward pool pump started making a humming

check impeller by turning shaft with pliers sounds as if its stuck do this while of and try to restart

SOURCE: my self priming spa pump wont prime

Bleed air from pump by loosening union nut until water emrges, then retighten by hand. good luck