Make sure the trailer is level with a bubble level when using the fridge, absorption type camping refrigerators won't work if not level. They use heat on the back to make coolant flow. If there is an access panel on the outside that lets you get to the fridge back check for it getting warm when plugged in and switched to use AC power.
Typically both AC and 12 volt power the same heating element, if that element is bad both sources won't produce heat. Propane
is a little tiny burner, size of the end of my thumb so even if electric element is bad, propane
may still work.
The wires for trailer brake, turn, marker lights
are often run in the same location as the camping 12 volt wires. Those cut wires in the picture look way too heavy for normal lights
etc. More like central location for converter and/or inverter.
Converter provides 12 volt and charges battery when your plugged into campground AC power so it needs heavy wire running to battery to deliver the charge. Inverter converts battery power to 110 AC to run things like a TV or other household appliance. Inverter needs a heavy wire because it draws a lot of current.
Not the same as the smaller 10 and 12 gauge wires that go to trailer lights and 12 volt camping lights, water pump, furnace
I would work backwards from existing 12 volt items, use some masking tape to make "flags" on the wire to label what the wire is coming from. You may find they all go to a common junction, wire or location.
E.G the 12 volt cabinet lights in my scamp
run on two wires that go down behind the ensolite to the same wires that provides 12 volt on the fridge. Those two common wires lead to tongue and is "main" line for 12 volt. There are colored wires running alongside those two wires, the colored wires go to the tail lights
Battery is typically mounted on the tongue where it can vent gasses generated when it charges. I would look for the original wiring to be running up to that location BUT my 77 scamp
(Boler cousin) did not have a battery or place to put one, it only had 12 volt when plugged into the tow vehicle. The "main" 12 volt line goes to the trailer 7 pin plug, which had been cut off, camping 12 volt wires capped and a 4 pin plug wired in for the tail lights
Work back from 12 volt lights etc. and forward from hitch plug and you can at least map out the existing wires.