To figure out what's what, we used to use a battery charger on the truck camper wiring. The negative clamp is hooked to a grounded pice of metal on the camper (trim?). The other lead is then used to check each lead - left, right, running, direct short will likely indicate you've located the ground, and when you find the power wire, the interior lights will work. Color of wire guarantees nothing, but generally you have the right plan.
Regarding the 12v fridge, we rarely wired them when was set up for it because they draw too much power. Run better on 110v and propane.
Regarding the power wire coming from the truck, your question is like walking through a mine field... In the most basic form, the power is lead back right from a circuit breaker or fuse connected directly to the positive terminal of the battery. The problem with this setup is the potential to run the truck battery dead with the camper lights. To avoid this, an isolater of some type is often used. I'm not going into that here. You can check on that further on your own. Or you could unplug the truck from the camper when you arrive at your destination...
Answering any question regarding an inverter is going to depend on it's size. There's a huge variance available.
1997 37' HR Endeavor, 275hp Cat, Freightliner
03 CR-V Blue Ox, Ready Brake