The Ring of Sauron

[Lord of Angmar]

I highly doubt that a Balrog would take the One Ring and claim it for itself. More likely it would simply give the Ring to Sauron and reap the benefits of living in a world where evil can run rampant, rather than challenging a much greater power and in doing so taking away strength from the fight against Gondor and the free peoples of Middle Earth.

where does the idea of Olorin binding Narya and Glamdring to his spirit?

Agreed. I see no evidence for that. We do not even know with any certainty that Gandalf had Narya with him. My guess is he probably left it in Imladris before setting out with the Fellowship. As for Glamdring, it may be that that is one of Tolkien's 'continuity errors', though I think a more likely explanation is that he used it to battle the Balrog on Zirakzigil. Even though he came back in his second iteration [Gandalf the White] after his duel with the Balrog, he was still physically atop the mountain the whole time.