Also depends on the inverter. Some do not like the battery negative bonded to the 120vac ground.
No damage to converter/inverter, just creates a power loop that will discharge the battery in a short time.
Put the converter on a separate switch or its own breaker as needed. Also need to to keep the water heater and fridge set to propane only. Again no damage just going to drain the battery in short order.
Lights are 12 volt. TV need 300 watts max inverter.
You can wire the inverter into the electric system with a 30 amp transfer switch on the main feed or with smaller transfer switch to individual branch circuits.
You may want to map out exactly what outlets and appliances are on exactly what breakers.
