That second hum that you get on the good amp is very probably a ground loop hum, I'm sure the internal 230V power connections in both amps are wired differently, nothing unusual.
Eventually you should correct one of them if you want to use both amps together on stage , but that's not the main point today.
Please post a couple clean close up pictures of that burnt resistor.
I guess it might be part of a "Zobel network" that often is soldered right across the output jacks, instead of in the PCB proper.
It may burn if your amp oscillates, which after that becomes unstable. That oscillation is inaudible, but it causes the audio signal to become fuzzy, dirty, and the amp overheats, eventually burning out.
Definitely hooking extra speakers without respecting the suggested impedance causes trouble.