I just finished WMF a couple of days ago, so I'll leave most of your comments for more knowledgable posters.
Perhaps one of the rings in the poem about Kvothe represents himself, a ring for all the names you know after all. We know that he has changed his. I thought perhaps it was the blood ring, flowing. Representing a part of him, and I also tried to connect that to the blood that is required to open the lockelss door, just a thought. I also entertained the possibility that the nameless ring was his, because of the danger suggested by elodin in changing ones own name. Perhaps he hasn't just changed his name, perhaps he's lost it. I really doubt a part of his name is what he's hiding in that box. I'm not even convinced it's \his\ box.
The seer creature is called the Cthaeh.
I'm not sure I get what you're saying about the ring, but maybe it's related to what I've been thinking about since finishing the book...
On his first hand he wore rings of stone,
Iron, amber, wood and bone.
There were rings unseen on his second hand.
One was blood in a flowing band.
One of air all whisper thin,
And the ring of ice had a flaw within.
Full faintly shone the ring of flame,
and the final ring was without name.
Is the ring of air the one mentioned in the discussion between Kvothe and Elodin right at the end of WMF?
Seven things stand before
The entrance to the Lackless door.
One of them a ring unworn
One a word that is forsworn
One a time that must be right
One a candle without light
One a son who brings the blood
One a door that holds the flood
One a thing tight-held in keeping
Then comes that which comes with sleeping.
I'll be back with more thoughts later...