You only need to prime the raw areas, spot prime. No need to remove any paint that is well stuck to the brick, this would be too difficult anyway.
The exact time between primer and paint depends on the primer dry time, this info is on the can label. Many primers dry fast and only need an hour or two of dry time. Of course humidity affects the dry time as well. If you are going to spend half a day priming you might want to wait over night before applying paint just to make sure everything is properly cured. While waiting for the primer to dry is a good time to check out all of the caulking, around windows and doors, and get that fixed if needed.
Answer for How many coats?
Hey, the paint is peeling in certain areas so once I get that paint off some of the house with still have paint on it and some will not. Does the part that still has paint on it need to be primed? If I'm thinking right this means that I don't need to remove all the paint before I add the primer then paint. Is their a time that I need to wait after the prime before I do the paint?
Answer for How many coats?
Generally 2 coats is plenty. The exact number depends on the condition of the original paint, type of new coating and the new color; if the original paint is in good shape and the new paint is the same type with the same color then this would be a maintenance coat to freshen up the surface (1 coat is enough).
The actual preparation steps you need to follow depends on the overall condition of the original paint and brick. Pressure washing can be used to remove loose or peeling paint but this is difficult and could cause severe damage, especially the mortar between the bricks. If your brick is in good overall shape just wash to remove dust, dirt and oxidized paint. If you have a lot of peeling use the pressure washer carefully. Experiment with different tips and different pressures, do not use the straight stream tip. The idea is to use the lowest pressure and still get the job done.
Paint and Primer; this idea is a marketing gimmick that many buy into. Primer is a totally different type of product when compared to paint that serves a different purpose. A true primer can't be combined with a paint to get a better product.
All good paints, that use good resins, are self-priming over many different surfaces and are always self-priming over the same type of paint.
If you wind up with a lot of exposed brick go a head and use a good acrylic masonry primer, many universal primers are good over brick. And make sure to read the paint can label carefully, it will specify when a primer is needed- even Paint and Primer products have recommended primers specified on the label.