Can I put up wainscoting on concrete brick walls that have been painted in my basement bathroom - If I can, can it be glued and if so what kind of glue?
You can do it but I think you'll run into problems as you get into the job. You're going to want to use nails or tacks to hold some of the wood onto the wall, like moldings, top caps, and baseboard. You can glue it all on but sometimes you'll want to tack the piece to the wall until the glue sets and all you'll have to nail to is either concrete block or a 3/16" piece of wainscot.
If I was doing it in my basement, I'd use furring strips on the concrete, hang some 1/2" drywall on them, and THEN install the wainscoting. You'll get a better job that won't fall off or some of the other problems you may face later on.
The glue to use is called Liquid Nails and comes in a caulking tube. It sets up over night and is easy to use.