a) The Flying Bedstead was a small vehicle for making manual repairs outside of the Nostromo that would have been used by Brett and Parker, but they never got around to shooting the scene, and so it seems that the vehicle was never actually made. Ron Cobb's design looks roughly inspired However. by the shape of the Nostromo exterior with the engines specifically.
b) Ridley's sketch for thing thing makes the vehicle look very single to the extent it might turn out to be like a cross between a child's go-cart and foldaway work bench
c) The name is taken from the nickname for a thrust measuring rig in 1954 that was a vertical take off and landing vehicle developed by Rolls Royce that was nothing much more than a machine with a frame