In regards to the hot water heating, you will always want to run it on electric if plugged in as it was save your propane. After all, you are already paying for the electric at the RV park you may be at. When you turn on the switch for the electric heating element, you will not hear it.
If you want to run on gas, their is also a switch for that usually in the same cabinet to turn on labeled WATER HEATER. IF you turn that on, their is an LED that tells you if it is lit or not lit. It has an auto start like your heaters.
In regards to power...You either have shore power or you don't. At one point you mentioned that the red light was on when you flipped the electric hot water heating switch. No it sounds like it is not. As you mentioned, nothing happens. (Are you referring to the other switch labeled Hot Water as mentioned above? ) Note, on the hot water tank itself you will see a switch also...it needs to be ON for any hot water to be made. May want to check that as again, it was more than likely turned off for the winter after the tank was drained.
Don't be disappointed in the fridge, you can carry much more food and in a propane one.
I have three A/C units, I can run all three at the same time. You should be able to run both of yours I would have to think without issue. Really, one would not cool that coach enough in the summer. I also have one thrmo, but it runs all three. You set them in the thrmo itself using the buttons to cycle though the settings for each unit and heater based on the mode you are in.
Side note...Their is a GS rally at the end of June in Goshen, IN where you kind find all kinds of people who can help you. Just mentioning as it may be worth the trip. Like 70 of us will be their. If you need info, let me know.