On the OD, when I took ol' gray, '90 F150 to haul the coupe home we were pulling the empty trailer and the tranny started shifting funny. A quick check of the truck manual said to never use OD when towing. We left it in "D" after that and it was fine.

My 2017 F150 has the Max Tow package (10 speed), and it's got 3 modes - Economy, Sport and Tow/Haul. The Tow/Haul mode restricts the higher OD gears.