Welcome to the forums Harry!
If this bath has a shower, I'd recomend removing the popcorn. While the popcorn may seem to be in good shape, unless it's been well painted, it is likely to turn loose if you paint it. The popcorn is easy to remove, just mist it with water and scrape. It does make a big mess
There isn't a good way to repair popcorn other than scraping off the area to be repaired, fixing it with joint compound [maybe tape too] and then retexturing. I have cheated and dabbed some caulk on cracks - still noticable but not as bad as before.
The vent should be plumbed to the exterior, either thru the roof or out a gable end.