Let's get back to what the OP wants:
"Looking at some f150's for hubby to use daily, but can tow. Will make some concessions on size and weight for TT. Maybe something around 5000lbs? Just looking for a towable bathroom and bed, living space isn't important as we like to spend time outside anyway.
What am I looking for in specs? I've included some specs below for a TV we are looking at. Dealer says about 2360 payload. There are 6 of us but we will be taking 2 vehicles to camp, since the kids are all older and almost out of the house."
Note that the OP does not plan to fill all of the seats in the truck and can even split up the cargo some since she is planning to take two vehicles anyway. The specified trailer target weight is 5,000lbs. Since a F150 with max tow package and 3.5 Ecoboost is rated to pull 11,000lbs there is a lot of room for growth. The truck will be used daily without the trailer. The Ecoboost has more usable power than the 6.2 found in the F250 and gives about 3 more mpg. My 3.5 Ecoboost does have LT tires under it instead of car tires but I would not hesitate to pull a 5,000lb trailer with it. In fact, I am pulling about twice that much with mine. Heck, I used to pull 5,000lbs with a Chrysler Newport with 6 people and gear for an extended vacation. We put about 60,000 miles on the car pulling the trailer with a 180,000 miles total which was exceptional life in those days. In all honesty though, expect your trailer to gain about 1,500lbs when loaded for travel.
Next question: "Gvwr 7000. Still a bit confused what the gvwr means for towing. 10-15% of the TT weight goes towards the payload in tongue weight, is that correct? Is that loaded or unloaded?" GVWR (Gross Vehicle Weight Rating) includes everything that came in the truck and what you add. It is what the scale will show when you drive across one while on the trip. So hitch weight, people, beer, mud, even the gasoline and wiper fluid. The other important weight is Gross Combined Weight Rating or GCWR. That includes everything that moves when the truck moves. The 10-15% on the tongue is as you are pulling it, so it changes as you load the trailer. A trailer that size probably has two axles and I try to visualize keeping my added weight balanced on the front axle or a little forward and that works well for me. Too little weight and the trailer will sway excessively so if you get too much sway stop and move some weight forward. It can get out of had and make you loose control while going in a straight line, I have seen it happen. You probably need a load distributing hitch and a sway control device with a 150. The flat sides on most campers seem to generate turbulence that leads to sway. I don't mess with sway control on other types of trailers but campers seem to be much more likely to need it.
Good luck!