In your control panel, there's a switch to check tank water levels. One of the indicators is for the battery charge. If the Power Converter is charging the battery, the indicator will always show 4 lights. If you have auto-leveling, you can cycle its control panel to show voltage which will be >13 V if charging. Or you can put a voltmeter directly on the battery terminals to check for >13V DC.
The Power Converter at times may consume up to 12 amps. So you don't have a lot of leftover capacity to run other things. You definitely want the water heater set to propane mode, not electric.