I have had a couple of instances of that output capacitor failing…. usually it’s caused by plugging the output of the P3 ito a mic input with phantom power on it (!) This usually damages the output capacitor and has been known to wreck the output stage!
The power supply for the P3 is not critical….. the internal voltages are stabilised. It’s normal for the power supply to measure between 11.5 and 13.5VAC The symptom for having too low a voltage is severe hum on the output.
Yes, the input capacitors are in use all the time.