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Short answer: 75W-90 of any stripe or 80W-140. That info specs synthetic, so on an older truck you might want to stick with dino oil in similar weights.
Any gear oil for hypoid gears will work, you don't need anything fancy.
How much? Not sure on the quantity, but it should run out the fill hole. 2 to 4 gallons is a wag.
Rezvani's Latest Post-Apocalyptic Monster Is a Ford F-150 Raptor Underneath
Slideshow: Called the Fortress, the 850-horsepower pickup combines Raptor underpinnings with military-inspired features, survival equipment, and a starting price of $285,000.