Jacks and slides can operate for many cycles on a charged battery. The issue is keeping the battery charged. Battery will discharge as the trailer draws power just sitting there even with everything "off". You need to disconnect the battery with a switch or by removing a cable every time it is not in use.
For the residential fridge the run time could be short unless you have four batteries fully charged. I would wait until you are hooked up and ready to roll to turn on the fridge inverter. Cool down is much faster than your old absorption fridge. If you stop at home to pack I would plan to plug in.
