Yes as MaddAussie put it, you're keying the surface, roughening it up slightly to give the paint something to grip onto better.
very few cases are raw steel inside, cases are normally made of SECC or SGCC steel both of which are covered in an outter layer of Zinc to prevent corrosion.
You can use a self etching primer as this contains an acid to eat into the steel surface slightly so doesn't need keying in theory.
Drying time between coats depends on the paint, follow the instructions on the can, remember that environment also has an effect, it takes longer for paint to dry in the cold than in warm conditions.
Generally speaking multiple layers or the same paint only need to be left for an hour or so between them, but leave it overnight between different paints (ie after primer leave it overnight before starting the colour layers and then leave that overnight at least before doing anything with it)
Acrylic paint generally dries faster than enamel paint but the end result is softer and more easy to damage.
What case are you trying to paint
btw?