Do you NEED to prime/

The water damage, YES, the spackled spots, yes, or at least 2 coats of finish.
If I were doing it, prime the whole ceiling with an oil stain blocker( cover stain) and 2 finish coats. For the walls, clean and scruff sand, clean and 2 finish coats.

Right now, the water damage has primer over it, and no water stains are visible.
I'm just wondering whether the paint will be absorbed differently in the spots/areas where there is primer. So, for the walls, if I put primer on the spackled areas and then TWO coats of paints, will the areas without the primer look different? Basically, if you use primer, do you have to put it on the whole area?
It's a fairly big area, basically three rooms that are open floor plan. The thought of putting three coats on the walls AND ceilings is daunting.

If you prime everything, you'll have a perfect outcome.
Doubt is eliminated....

ESPECIALLY if you're doing the painting.

I fully agree with Christophern's recommendation.

Faron

I pretty much agree. I think if you are using flat paint on any ceiling and you have some patching that you did up there, either use the actual flat paint to prime the patches or prime the entire ceiling. Spot priming on a ceiling with an actual primer is just asking for a flash because now you have sealed that area and the rest of the ceiling is not sealed. Aside from the patching issue, if you are going for the perfect looking ceiling, you will want to prime the entire ceiling and then apply one coat of flat. The primer will give that flat paint the extra open time that you need on a ceiling, plus it is just easier to paint over a primer than it is to paint over another flat paint layer. All of this is particularly true for a novice painter. Priming just makes everything easier.