Not all primers are created equal. Apply the primer, and wait the recommended amount of time before applying paint. Just for reference
SW Preprite 200 Primer (good for drywall) will dry to touch in 1 hour, but can be recoated after 4 (at 77 degrees F, 50% relative humidity). Know what happens when you try to put more paint on a wall that isn't ready to be recoated yet? The solvent in the coat you are applying destroys the weak bond that the coat below has on the wall, and it comes off!
As for the ceiling, you can use ceiling paint if you want to deal with separate cans. The only benefits are a slight price reduction and a slightly thicker formula to prevent drips. IMHO, it's not worth having to buy extra gallons of paint. You can use the wall paint on the ceiling if you want the same color and sheen.
Ceilings have to be primed, and you can likely use the same primer you used on the walls.
Yep, recommended system on most wall paints is 1 coat primer and 2 coats topcoat.