As a quick reply to help you with your water heater:
* Remove and bypass the fuse link or thermal fuse. This is that 90-degree looking WIRE thing inline to one of the thermostats (It think.) Then see if the flame stays lit?
* If no joy, then bypass each of your WH thermostats one at a time and see if your flame stays lit?
* If not, then post the type of water heater you have so those "in the know" can help you diagnose your problem. ...Usually it's the thermostat, thermal fuse, or circuit board (in that order).
Regarding your windshield wipers:
* Loose articulating arms? ...This will be obvious if your motor is working but your arms are not. ...And be careful not to put your hands in that area when another person turns the wipers on/off!!!
* Is your wiper switch part of your steering wheel assembly? I.e., you need to rule out a switch problem after you verify your fuse is good.
Note: Wiper fuses often fail in cars due to over loading, but the other reason a wiper motor does not turn "on" is because the motor is NOT getting a good ground. ==> To fix this you can just add a ground wire from one of the wiper motor nuts... and connect it to a good ground. ...And 50% of the time this will fix your motor problem.
I don't know your type of RV but hopefully you will examine your problems closer and then someone who knows what you drive can offer some better suggestions.
For now, I'm guessing your first priority is to get the hot water heater working. Good luck.