Hello, welcome and congratulations!
Do not worry, these things are not rocket science. You will be fine.
The answer to most of your questions: Yes, maybe, in principle. Without knowing your camper, the appliances, how they are set up, and what has been modified since 1994, definitive answers are difficult.
Let me try to give you a general idea to get the discussion started.
Your questions on battery charging: Typically, the built-in charger of the power center (the box that has all the fuses) of the camper will charge the battery when you are plugged into AC.
Usually, the battery is charged when the engine is running. There are a number of reasons why it might not be, though. It will not be overcharged.
Hot water: your typical water heater works on LP and may have an additional AC heating element. There should be a way to switch the heater and the element on and off. Newer campers usually have these switches near the water pump switch inside the camper. But in my 2002 camper, I had to go outside and manually light the water heater. It did not have an AC element, but when you have one, I am sure there is a way to turn it on and off. What your manual is telling you: Never, ever run the heater in either mode when there is no water inside.
The fridge: Most run on AC or LP, many also on 12V. Many have an automatic changeover mode where they automatically switch to AC when you plug in. Some do not, and you need to switch over manually.
To get better answers, you could give us the make and model designation of the appliance, or maybe post a picture. Picture posting here requires you to upload and link the picture. You can use
http://photoposting.is-great.net and follow instructions there.
best wishes, -J
2014 Ford F350 XLT 6.2 SCLB + 2017 Northstar Arrow