Well, some accurate info and some not so good.
First, yes you need 12v to run the water pump and landing gear.
Second, do you need to have the batteries on when connected to shore power? That depends on the converter. Some need a battery connected and some don't. Ours doesn't need a nattery connected to supply 12v for the water pump, lights, etc.
Third, always leave the batteries on when connected to shore power. That depends as well. Does your converter need a battery connected to function properly? Is your converter a smart multi-stage converter? A dump converter can over charge and boil the batteries if they're on and connected to shore power for an extended period.
Are things working as they should? You need to find out what type of converter you have then go from there.
