Yes, the A/C is AC (bad pun) so it only runs when plugged into shore power or on the generator.
The heater is propane. When you turn on the propane tank, light a stove eye first. That flushes the air out of the propane lines and ensures that the heater will light. You don't have to do that every time you run the heater, just when you open the propane tank after having it shut off.
Both the water heater and the refrigerator run off propane too, but each may also run off of 120v AC. Some do, some don't. Usually, the water heater has 2 separate switches, one for electric and one for gas. You can run both while showering or using a lot of hot water for faster recovery. The refrigerator usually has an AUTO setting, a GAS setting and OFF. If set to GAS, it only uses propane. If set to AUTO, it uses electric when plugged in or on generator, and uses propane otherwise.
Bobbo and Lin
2017 F-150 XLT 4x4 SuperCab w/Max Tow Package 3.5l EcoBoost V6
2017 Airstream Flying Cloud 23FB