Dorset Towel Ring in Chrome

Yes it swivels but not by design and not in a way that is helpful. The movement makes it more difficult to use it. The towel holder moves when you use the towel because the item will not stay in place. The movement causes marks on the wall as the towel holder rotates.

If you're referring to the tiny set screw underneath the cap, I had that problem at the beginning. My towel bar had the set screw already installed, but it was all the way in, so, yes, nothing "held." Before you attach anything to the wall, experiment with the set screw. Unwind it so the part that attaches to the wall easily fits in it. Then screw it tight and get an idea of how far it needs to go in to hold that part. Then unscrew it till the wall part easily comes off, attach to the wall, and then add the cap. It's tough to tighten the set screw then, but with a lot of patience and acrobatics underneath the towel ring, it will go in fine. Hope you don't give up! It looks great on the wall.

No. When I bought it I was hoping it could be switched to the opposite direction, but it worked out fine with the opening to the right.

Thank you for your question, there is just the one style.