How to repaint an antique exterior door?
Do I need to sand or is a good wash down enough? Or maybe a liquid
  sander? 


A good wash, followed by a thorough drying, followed by a light sanding with fine grit sand paper to rough up the existing surface.  Sanding ensures the new paint will get a good grip on the old paint.


  Do I need to prime, or is the old paint (cleaned a bit) good enough?


No, its been sealed long ago - just clean and sand.


  Is there any special paint, other than exterior trim (probably satin
  or semigloss) to consider?


Since there's already latex on it, exterior latex should be fine.


  Is there any additive I should use with the paint for flow, finish,
  hardness?


No.


  Do I really need more than 2 coats?


If it were white over black- you might need 3.  Black over white, you might only need one good thick coat.


  Is there something else I am failing to ask/think about?


Get saw-horses.  Lay door flat on saw horses.  Remove door from hinges, remove all hardware, tape all glass.  Paint ONE SIDE only at a time, let try completely, then paint other side.