Yes on Fords, the batteries are only connected when the switch is in the on position. And yes. If you have the towing package relay installed on your Ford. It in fact charges the trailer battery as you drive down the road.
As to your electric trailer jack. If your trailer battery is dead, all you have to do to power the jack. Is connect the 7 pin, and turn your truck key to on. Then the truck will send power to the trailer, and power every thing in it, that runs off battery. It's best to have the ruck running when you do that.
