If a pickup tube in the gas tank were disconnected or maybe cracked, that could explain why the engine quits after the fuel level drops (to a point where the fuel pump is pumping air). The fuel pump draws fuel from the bottom of the tank. But that doesn't explain why the engine runs if you hold a little accelerator pedal. Is the fuel tank vent tube plugged somewhere between the fuel tank and the charcoal canister? Remove the fuel filler cap to see if a vacuum in the tank is causing a loss of fuel supply. Is the carburetor getting adequate fuel?
The bed has 2 pieces of flat stock welded into a saddle shape that sits over the frame, like this., and depending if you want the attachment to pivot or not, you could use 1 pin on each side and a latch, or 2 pins on each side if you don't want it to.
I would say using a quick pin system would be the best, that's actually how the bed of my Mule is attached to the frame. Have corresponding holes drilled into the frame, and the attachment.