Indeed a very long time, HerenIstarion! Good entrance on the matter, especially your second point.
I've got some points to add now too.
1: I agree with HerenIstarion that the Balrog would not recognise Narya as Narya, but he would certainly know that this was something of great worth.
2: I think the Balrog could indeed have found out it's powers, but was unable to use it. Seeing the size of the Balrog and the size of Gandalf. Narya wasn't the One and, as far as I know, wasn't capable of taking a greater rounding.
3: You're dubious one, HI
- I disagree with you there. Sauron had neither one of the Three or the One, so I don't think he could have felt it in this way. I doubt if their was a special link of thought between the Balrog and Sauron. Sauron would eventually know that the Balrog had Narya, but I guess that would be just by mouth-to-mouth-talk of orcs.
I do believe that, once Gandalf was dead and his ring unhidden (or when it changes owner), the other two bearers, Galadriel and Elrond, would sense it. They both have one of the Three and use them full-time, this being the reason that I don't believe that Frodo would sense it through the One Ring, for he did not use that Ring.
greetings,
lathspell