The exterior cooktop is hooked up using a gas hose with quick connect ends that come with the trailer. The supplied hose has nothing to do with the third tank.
The way they designed the outside kitchen, and where the gas line is, kind of prevents having the cooktop connected to the gas line all the time. That's why they included the hose--to hook it up as you need it. The hose is also used for the grill, if you got that option. (Not sure if you get a second hose with the grill or not, since I don't have the grill option).
My truck tows the trailer just fine. Mines a 2wd with 4.10 gears. The 377 is a big trailer but my previous trailer was the same size so I was already used to pulling something that big. In fact, I pulled it with an 05 F250 with 3.73 gears and it was fine. I just wanted some extra safety and stability. I have air bags on the truck to level out the ride. I've also done a couple of mods to the truck, which help my towing experience. If you've owned a 6.0 for any length of time, you probably know you need some type of gauges to monitor your engines health, a free flowing exhaust (cat delete, straight pipe, or upgrade exhaust system), and handle the egr systems weakness by either deletion or upgrade to a bullet proof unit. Also, get a coolant filter.
Good luck with your new camper. Feel free to ask any questions
2016 North Point 377 RLBH
2006 Ford F350 Lariat, CC, 6.0PSD, DRW, SCT tuner, air bags, bullet proofed