Ceiling fans usually wobble if they aren't mounted or installed correctly. So that would be the first thing I'd recommend checking. Get a ladder and inspect all the screws and bolts and everything to make sure the fan is secured.
Insulating batts are usually made of fibre-glass that is loosely spun. Tiny slivers of glass fibre can easily break off and penetrate the skin to cause pain, irritation and inflammation....
If it's possible that your ceiling contains asbestos, I highly recommend that you hire a qualified and certified asbestos removal professional to avoid any problems.
Painting over a popcorn ceiling is a way to "encapsulate" asbestos, which will contain it. Spray paint is best so that you don't disturb the popcorn ceiling and make it...
It's unlikely the wobbling was related. If the fan is super old, it could be a problem with a motor. If your fan isn't ancient though, it's almost certainly going...
The only way to "clean" a popcorn ceiling would be to paint it. And that will be a somewhat messy but rewarding chore. The "popcorn" elements you see are added...
First, check to make sure all the screws on the fan and ceiling mount are tight. If it's still wobbly after that, I would recommend using a blade balancing kit...