Ford F250 6.2L V8

Might be fine in Indiana, but if you're out in mtn country I don't think that 6.2 would be any fun. Big difference between the west and the Midwest.

Yes you can. With no problem other than not so great fuel mileage. You have a very good truck with a great motor! How do I know? That's what I had and pulled with prior to the truck in my sig. Only reason for changing was I just missed the diesel torque having been in a diesel since 2002 prior to the 6.2 for a year and a half. Well, that and planning on a larger rig in the next year on two. I averaged around 9 +- mpg towing with it. Good luck!

I have a 2013 F350 Dually with the 6.2 gas engine and 6 speed trans and 4.30 gears. What an awesome combination. Traded a 2006 F250 6.0 Diesel for this truck with no regrets. I use both of these trucks to pull a 34' gooseneck horse trailer with living quarters which weighs about 14,000 pounds loaded per the scales. The gas engine pulls it just as well at the 6.0 diesel did and averages 8 mpg driving the speed limit on interstates. As noted above, make sure the pin weight doesn't exceed the factory spec limit - the weight should not be a problem for the engine or the trans though. Enjoy.

With 5th wheels the question generally not what it can pull, rather what can it hold weight wise on the rear axle. Known as "pin weight".
A good ball park figure is 20% of trailer weight but it is getting larger the past few years with bigger fivers.
Having said that I've seen much worst combinations all the time. You should be fine IMO at those posted weights.

There is certainly lots of info out there.. Hopefully you have found things that are pertinent.

I found this:
Capacities

I just bought the same thing you did, F250 with the 6.2 and a 3.73 rear end.

I would not hesitate to get a ~9500-10k lbs 5th wheel. Truck is rated to pull 12,100 with the 3.73 rear end. So at 10k, you have a 20% margin, which would make me feel very comfortable.

GCWR is 19000ish. Tranny is pretty heavy duty. Next year, the gas F250 is supposed to get some tranny that was left over from when the F150 offered the 6.2 L motor a couple of years ago. This is the reason I bought a 2016. Still had the Torqshift in the 6.2 L gas.

The truck has a 3.73 rear end..

The truck certainly seems to be rated to take a fifth wheel of that size. Certainly does depend on your final gear ratio, and of course that will affect mileage and RPM's too.

You will be slower than some in the hills, diesels don't lose power with altitude like gas engines do, but you will be OK.

we have a 5th wheel that weighs ten thousand pounds loaded . we pull it with a 2013 Ram 2500 HD with the 5.7 hemi and 3.73 gearing
does a good job . flat terrain I can cruise 62 MPH turning 2000 RPM
hills it downshifts as it should , but the 6 speed trans takes care of the downshifting with ease . we get about 8 to 9 MPG towing . we just did a 1000 mile trip to the outer banks and back .no problems
yes , diesels are great for towing, but the extra cost for a diesel can buy a lot of gas . I think you will have no problem pulling that size 5 th wheel. good luck what ever you decide.

Correction cargo capacity is 2920lbs.