Yes, they make “sealed” insulation, google “encapsulated insulation”.
The ceiling, consider leaving it open and renting or buying a high volume paint sprayer and just painting it all a light color. I did this in my semi-finished office/gym in my basement and I’m happy with the results. It is a bit industrial looking, but that fits with the basic theme here, and it was waaay cheaper than any of the other options. I also have a fairly low ceiling and didn’t want to lose any more height to a dropped ceiling. Drywall was never an option, it would bury too much crap that might need to be accessed.