The Volt & Hertz meter on the 531A is upstream of the breaker, so they will read if your generator is making power, even with the breaker off. The diode you mentioned acts as a surge suppressor across the shunt trip coil in the breaker.
The breaker shunt trip coil is controlled by the A2 engine controller, which trips the breaker on overload, and also stops the engine on low lube oil pressure. This module is powered by the flywheel alternator, hence the breaker tripping only when the engine runs. The breaker shunt trip is triggered by the A2 module if the output voltage drops too low, as in the case of a severe overload. Since there is no power being made by the generator, the A2 module "thinks" that there is a severe overload and trips the breaker. The trip you are seeing is normal if there is no power coming from the main generator.
There should be no movement of the stator rivets. I would recommend dropping the control box down, and opening the cover of the generator to see if there has been any contact or damage between the rotor and stator. The stator to housing is a tight fit. If there is any movement that could allow rotor/stator contact, that would cause severe damage. Any movement of the stator in the housing needs to be repaired/stopped.
Your main troubleshooting at this time should concentrate on why the generator is not producing power. Either a A1 module, wiring, or generator issue.
The back of the manual has the schematic to help troubleshoot.