Let me try to explain this a little better. The percentage of tongue weight vs overall weight is to have a trailer with less sway. You want tongue weight. That number could vary from 10-15% maybe more.
Trying to do this math without scale results is just putting you in the ballpark.
Sounds like your truck will be fine with the models you're looking at, as long as you get the correct weight bars. Another words, let's say the camper has an "advertised" tongue weight of 1000lbs you would need 1000lb weight bars, maybe 1200 considering the nature of your tow vehicle.
For example I had 1000lb bars with a 750Lb tongue weight. But with a 42 gallon tank behind the axle, heavier bars will help.
As far as the tire question. Think about the guy with the 3/4 ton truck running E rated tires pulling the pop-up camper and I think you'll get your answer.
But, make sure that Burb has E's on it.
2018 Ram 3500 DRW CCLB Aisin 4.10 4x4
2018 Jayco Talon 413T
B&W Companion