What is a good kind of glue to glue small pieces of drywall that are too big for mud patches but small enough that driving a screw through would crumble the drywall piece?
Any common construction or project adhesive. That said, drywall nails are fairly thin for just that reason. If it's large enough that you're installing a patch, a nail won't destroy the patch.
And that said, it's often the easiest solution to simply enlarge the patch to something suitable for repair, say 6" x 6". Float some one-by lumber or plywood scraps for backing and be happy.
Run the screw in reverse until it drills a hole for you in the drywall. Then sink it carefully.
Down to the size of about 1.5" strips you can still use screws with this method. For anything smaller I'm partial to construction adhesives that act like liquid nails.