Your fuse / breaker box is actually two electrical systems. 12 volt DC system uses the fuse panel and 120 volt AC uses the circuit breakers. The 120 VAC passes through the breakers to power up the converter, AC outlets, and air conditioner. Your fridge is connected to both. It is plugged into an outlet (hidden outside) and wired into 12 VDC system for gas operation. If fridge is set on auto, and you are plugged into shore power, it is running on 120 VAC, and completely seperate from your lighting system.
The lights are 12 volt only. They get power from your battery, or, if plugged into shore power, directly from converter.
The listed symptoms don't make sense, unless there are problems with both 120 VAC and 12 VDC systems.