Welcome to IRV2 !
You are correct the 120 volt outlets will only work when connected to shore power. The 12 volt outlet will have power supplied by the battery. the battery should have enough capacity to run the electronics for the refrigerator, water heater, water pump and lights. Remember that placing a additional draw of a inverter and television will dramatically decrease the charge on the battery.
God luck on your Jayco purchase. We had a 05 Jayco 23B and loved it.
Gene & Ginger
1997 Jayco Eagle 8
04 Winnebago Adventurer 33V, 05 Jayco 23B, 02 Coleman Cheyenne