Can I infer the amperage rating of an electrical panel from the pump motor rating?
This looks like a 3-phase contactor or motor controller wired for 240V single-phase (or to be more precise, split-phase). 

This is not the service panel, it's not the circuit breaker and it has no bearing on circuit capacity.   To get your answer on ampacity, you need to go look at the service panel where the breaker is. 

Jusging by the motor amps you are mentioning, this thing should be more than able to handle the draw of your new motor.