The converter should run automatically when plugged into 110V. It sounds like you might have an older manual for the converter. It will charge your battery and supply 12V power to everything in the trailer (lights / fans / furnace / etc ).
The switch next to the converter is almost certainly the water pump switch. It's a pressure demand system and should only cycle when the pressure falls below a setpoint. Don't run it unless you have water in the tank and you don't need it when hooked up to city water. When using it, you will hear it pump until it pressures up and then stop. When you turn on any water and the pressure drops, it will cycle back on. If it keeps coming on when you aren't using any water, look for leaks or an open faucet (usually the outside shower).
Most of the premiers I believe had 3 way refrigerators (it MIGHT be a 2 way). In the access panel on the outside of the trailer, you should have 2 or 3 sets of controls. One should be marked 110, one 12V, and there should be a knob for propane and an ignitor button. You might have a slightly different setup depending on the model. It MIGHT be auto-switching with controlls on the refrigerator itself. If you can find a model number, you can probably download the manual for it.
The refrigerator: They don't cool down very quickly, so plug into shore power the day before you leave and let it cool down. If it's not auto-switching, don't turn on more than one power source at a time. Don't put anything into it that isn't already cooled down (I always put a few drinks in mine before I closed it up and turned it on the day before, then put everything else in an ice chest until we got there). If it has a 12V option, DO NOT use it unless you're hooked up to the TV. It'll kill your battery in a few hours. Also, don't leave it on 12V if you're going to be stopped somewhere for more than an hour...it could drain your car battery to the point it won't have enough juice to start.
2012 Chevy Tahoe LTZ - HD tow package
2017 Rockwood 2703WS Emerald Edition