If your trailer is the same as my Coleman you do have LED lights already with the exception of the hood over the stove so you should be good there.
Your 6 volts are good. Since it sounds like you will be doing your camping during the summer it should be antiquate for several nights of limited lights and TV use but keep in mind if you use your furnace it will draw the batteries down very quickly. You should get a better battery monitor one connected directly to the battery. It can be simple with a LCD readout and low battery alarm. I use a Voltminder. Yes, there are more sophisticated monitors out there but your not running solar so you don't need that expense. I hard wired mine directly to the Converter where the battery cables connect.
Digital Voltmeter | VoltMinder.com
I use a 175 watt SAMLEX inverter for running my 39" LCD TV. I wired a 12 volt outlet near the TV station directly to the converter with 12ga wire. It's quiet. Some small inverters have loud cooling fans that you can hear over the TV.
Generator time use to be 8am to 8pm but alot of parks have extended to 10pm. For me it would depend how close you are to your fellow camper for running after 8pm.
What kind of tow vehicle do you have Truck? Can you carry your MB there? If not for a platform rack my first choice would be one from Lippert. It connects to the trailer frame and not the bumper.
My second choice would be the hitch platfrom sold by Harbor Freight and use a 4" 2" bolt on receiver for your trailer bumper.
I had done this on a trailer I use to own. I also used bumper struts for strengthening the bumper..
You don't want the rack slopping around back there so you want to get a hitch vice like Hitchrider
Hitch tightener: no wobble, anti rattle stabilizer device for hitch accessories