Its not your 30 amp electric at all. If the microwave works, the 120 volt system works. A 30 amp system is as simple as that.
Your space heater and hairdryer are 120 volts only and don't need the converter.
Your AC is 120 volts but needs 12 volts to operate the thermostat. Same with the fridge, if gas/electric.
On to your converter/charger.
Its ok to have 2 and 3 chargers on one battery. Folks with solar, engine charging, and the generator running do it all of the time. All charging is regulated by voltage to not overcharge your battery.
First, some converters are plugged in and may be plugged into a GFCI circuit. Check for thr plug out and then all of the outlets for a test reset button. Do this while plugged into shore power. They don't reset without power to them.
Second, many converters have 2 fuses in them. They are called reverse polarity fuses. They blow if you connected the battery backwards, even for a second.
Sounds like a $10 volt meter for testing is in order. You probe the battery cable connections to see if you have 13.4 volts at the battery when on shore power. 12.6 when not.