I know you replied with questions but going to skip those for now. Smarter guys than me are going to read your replies.
Pictures of the trailer would help to get clever with inverter placement. Especially where your circuit breakers are and also a panel with all the switches.
Dont need a close up. Further away is better. The goal is to find the best spot to get 12v power, instead of running wires from the batteries directly. You already have a ton of 12v inside the trailer. To run a TV you wont need much so you can borrow power from something like a powered awning. Fuel pump. Rear exterior lights you never use.