Is work done when falling towards earth while

You betcha !

-- Work is done whenever a force acts through a distance.

-- The skydiver has weight.  That's the force acting on him.

-- As time goes on, I'm assuming that he falls from one height
to a lower height.  That's the distance the force acts through.

-- The work done on him is  (force) times (distance)

                                           (his weight) x (distance he falls).

So where is the machine that does all this work ?

-- It's GRAVITY that does the work on him as he falls.

So how did he get all this energy in the first place ?
Where did it come from ?

-- From the airplane that lifted him up to height from which he jumped !