Yes on both accounts.

That first number—1980 pounds—accounts for anything that was added after the factory other than a full tank of fuel, including:
* driver
* any passengers
* any after-the-factory accessories—bed liner or rug, floor mats, heavier-than-stock tires, etc.
* any cargo, including things like tie-down straps, first aid kits, and other stuff some of us like to carry
* anything in the bed, such as the Teryx, ramp, etc.
* tongue weight, including the weight of the hitch itself
It's derived from the total GVWR (probably 7050 pounds or thereabouts, and also listed on the white sticker) less the factory curb weight, and it's usually a lot more accurate to go weigh the truck with a full tank of fuel than to guess how much weight you carry around beyond the factory number (e.g. I never would've said I carried 35 pounds of recovery gear until after I weighed the truck and started trying to figure out where my payload went).

As far as axle weights go, yes, that's the total weight that the tires should be supporting for each axle.

Very few half tons can haul 1500 pounds in the bed while towing a trailer of significant weight and still remain within spec. If I were in your boat, I'd be looking at an F250 gasser with the camper package or an F350 SRW, depending on how much of a PITA factor being over 10k GVWR was going to be (the F350 will buy you more payload headroom, but depending on your state and your uses for the truck, you may end up needing to jump through additional regulatory hoops because you're over 10k GVWR).

 

Actually incorrect
there are three Weight Ratings on the white sticker

Gross Vehicle Weight Rating (GVWR)
Front Axle Weight Rating (FAWR)
Rear Axle Weight Rating (RAWR)

FAWR + RAWR is NOT Equal to GVWR

This is a built in reserve factor. You should not max out both axles at the same time. The ratings per axle are higher individually to account for specific loading requirements and provide a reserve.

For example mounting a snow plow on the front or maxing out with concrete bags for a project.

Here are the numbers from my truck an HDPP.

GVWR = 7850 (This is the most my truck should ever weigh It won't blow up if I exceed it but on the off chance I should ever get stopped by the real weight police these are the numbers they will be looking at.)
FAWR = 3750 (This is the most the front axle is rated to withstand (Without exceeding GVWR))
RAWR = 4800 (This is the most the rear axle is rated to withstand (Without exceeding GVWR))

FAWR + RAWR = 8550 which is greater than GVWR by 700 pounds

I can put 4800 pounds on the rear but that means I can only put 3050 on the front. (And have a VERY Light front end. And I beleive not possible on my truck as I have a 4x4. Empty I'm in the 3200 range)

Conversly, If I load the front with 3750 (4x4 with light Winch and light plow for example) I can only load the rear with 4100 and stay under the GVWR.

Every truck winds up being a little bit different. It's best to get to a scale and get known weights empty and full and make educated decisions regarding loads.

 

"The towing capacity is 12,200, and the payload capacity is 3270".

I'm stunned.

 

Unfortunately, that means you are basically at full payload capacity with just the toy in the bed and two grown adults.

Few realize just how sensitive half ton trucks are to payload capacity. They may, in theory, be able to tow a lot, but they are still half ton trucks. Ram and Toyota have even less payload and GM seems to be fairly similar to Ford? Basically none of them are built to do what you have in mind.