Etrailer sells tow mounts for each which is interesting because I never thought about flat towing a big truck like a F250, F350, or F450!
Based on info found on Ford-trucks.com, the manual for a F250 says unlock the hubs and put the transfer case in neutral. I have to assume it would be the same for a F150 if you had unlockable front hubs, and you seem to need the manual transfer case. It doesn't seem to matter if the transmission is automatic or manual.
Weight ranges from some quick searches.
2016
F150 - 4,049 to 5,236 lbs
F250 - 5,941 to 6,942 lbs
Obviously, 4 wheel drive is heavier than 2 wheel drive, more doors weigh more, more options weight more, and heavier gasoline engines and diesels weigh more.