Yeah the Healing Rings are incredibly useful, I use barely any food thanks to them.
They don't save you from dying in one hit, though, so if you march to the last dungeon with a low lv char you can still die.
The Healing Rings only trigger upon taking damage while the Meditation Rings only trigger while using a skill.
So yeah if you have 0 energy the ring won't do anything since you can't use a skill to trigger the ring.
Purity Ring seems to trigger even if you put it on when you are already paralyzed and it immediately removes the paralysis.
Kinda limited usefulness, imo.
I've never used Graceful ring so no idea what it does...
I'm guessing you don't lose energy if your skill gets interrupted before it works.
Why not use Meditation Ring instead?
Thief's Ring disables traps.
I forgot if it affects floor ones but it does disable chest ones.
You just see the ring trigger and then it either stays intact or breaks.
Mystery ring: Dunno. I made a thread about it not far from yours!
Wouldn't have made it if your thread was already on my sights.

Edit: oh, mine was first. ...by a tiny bit. nice timing.