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Just bought a 2014 270 Vantage with the summer kitchen and I have a couple of questions re: electrical and battery that don't seem to be explained well in the manual

1. When plugged into shore power, it clearly charges the batteries that drive the inverter that drives the grill, but..does it also charge the engine/starting batteries?

2. The refrigerator seems to be able to operate 2 ways. I assume this because there is an AC plug that seems to be able to be plugged into the outlet that is powered by the inverter. If this plug is not plugged in, the refrigerator runs when the batteries are on. I assume it's running in DC mode and draining the starter/engine batteries in this mode. I also assume that if I plug it in the AC outlet AND turn the inverter/grill on, it will run off of "AC" power supplied by the batteries that drive the inverter. Is that true?

3. When in my slip and plugged into shore power...can I charge the batteries that drive the inverter AND run the refrigerator off the inverter at the same time? Is this what most people do?

Thanks so much in advance, it's all a little unclear.