perhaps you should take it to motor shop ( google motor rewind and repair in your area).. Electrical motors that run in water should be repaired by insured shop.
The pump motor should have a label on the side of the motor showing a diagram for Common, High speed, Low speed and the right positions for the connections.
Common is always the white wire
High speed is normally red
Low speed is Black
Green wire is always green
Most likely the run capacitor yes. Some motors have 2 capacitors, some one, some a combined start/run capacitor.
Replace it with one the same or greater voltage, and the same capacitance.