I gather that "100 volt" means using an adapter to plug into a 20A plug (standard household type). BTW this is a 120V plug just like 30A and 50A (50A is more involved).
So the charger, refer and some plugs now work - lights are 12V, different circuit. This suggests that everything that bypasses the EMS is working. That's good as you want to keep the batteries charged. Certain appliances like the charger and refer should always get power even when the EMS shuts down big loads like A/C, HW, etc.
So why do the plugs and TV work? I suspect that your Magnum is an inverter/charger that has a AC transfer switch for it's AC and it's inverter. So since the charger is working and has AC the Magnum passes that power through to the output circuits.
My Magnum has 2 output circuits. One is for the MW and the second feeds most but not all of the rig plugs including the TV.
I think your EMS is bad and ATS OK.
But you posted that nothing works on 30A or 50A correct? That has me wondering about a second problem possibly even the pedestal.
Based on your posts I would not advise checking voltage with anything other than standard 20A plug in devices. Get some help.