Pool pump immediately trips breaker - bad breaker, bad capacitor, bad pump?

You should probably change breaker even though u got pump working. Breakers are only made to trip a certain amount of times before they lose resistance. Your breaker will probably will be fine for years but for 20bucks it’s worth changing. You are protecting a pump that cost much more
 
I confess to not having read your entire thread here. But I did have a situation where the motor tripped the breaker immediately after the motor was started. It turned out to be the stems of oak leaves stuck in the impeller, thus making it unable to turn and binding up the motor.
 
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