"Nubs" wrote

The garage is under the house, has concrete block about half way up, and
the rest is drywalled. Originally, the builder rolled/sprayed on a thin
coat of mix, and dragged a roller through it.

I had painted interior paint on the walls. Now, since washing the vehicles
inside after many years, the mud is peeling in places from the drywall.
The garage is not heated, but stays warmer than the outside air
temperature.

Can I use exterior paint on the drywall? Do I have to use a primer on bare
drywall where the mud has come off? Should I primer all areas, even the
area where the mud/texture has not come off?

For a long lasting finish, yes you need to prime the drywall. All of it for
the best finish. Be sure all the mud is off but dont get it too wet in the
process. Let completely dry, then prime and use a paint over that meant to
be 'washed' (exterior will do)

One last point. Can I use exterior paint on the concrete block? Should I
prime the block, which has never been painted?

Yes, and again prime first. You may find the best to use here is stuff sold
for basement cinderblock. It's thicker and easier to add to a pourous
concrete block. It will likely take 2 coats with a thicker roller.

If a brand name helps, last time I was involved with this, Mom got only
Sherman Williams (sold at sears). I am sure there are others as good, but
this one worked for us in a somewhat similar need.