A: Of course you can paint them! You just have to be careful while doing it.
The absolute best way is to use a paint sprayer. Unfortunately this just isn't an option for most people. The problem with rolling the paint on the ceiling is the moisture from the paint can cause the texture to release from the ceiling. You can be rolling along and all of the sudden the texture will wrap around your roller. Not only does it get texture in your paint, but it leaves a big bare spot on your ceiling!
There are special foam rollers that are designed specifically for rolling paint on this type of ceiling, but I have bever personally used them. I don't know if they are any better or worse than a standard roller cover.
If you choose to roll paint on your ceilings, plan on applying two coats. Don't let the roller or ceiling become too saturated with paint. Allow the first coat to completely dry before applying the second coat, this will reduce the likelihood of the texture coming off.
If your ceilings are stained you may need to prime them first. Water stains just need a little Kilz from a spray can. If you home has been smoked in for years and years, you may need to roll Kilz on the entire ceiling as the stain will continue to bleed through several coats of paint.
I like to use a low grade flat white paint. Cheap paints are clay based and dry much more evenly that acrylic paints. This is about the ONLY place where I recommend this type of paint!