Oh yeah, drywall dust is the worst! I've found those vacuums that attach to the sanders are very effective. Good luck!

It's a stipple or stomp ceiling. Achieved by dipping a sponge or brush into drywall mud and creating a repeating pattern all over the surface.

As others have said, wear proper ppe, and wet a test area and see if it softens to scrape most of it off. If not, rent a sander and dust extracter and sand it down. You'll likely have to sand either way to get a consistent paintable finish