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.
It sounds like you could simply cut/have cut drainage channels from the problem areas to the front of the slab, or do that and also have a trough drain installed along the front of the slab. I'd start with the simpler/cheaper approach first - simple job with a diamond blade and a grinder or saw.
Best Answer
I'm going to make this a little simpler than some of the comments you have gotten and say that it's really as easy as priming and painting with a good quality exterior house paint.
I would clean the surface well from dirt, oils and other contaminants and then prime with a exterior oil based primer such as this Zinsser Cover Stain primer (random selection I'm familiar with, but just an example). It comes in quarts and gallons and will probably be cheaper than a specialty metal paint.
Once primed, you can use a quality exterior house paint tinted to any color. This is a very common way to paint the doors to match house and trim colors, and should be a long lasting solution.