Good guys of LOTR clueless?

[The Saucepan Man]

I do not seem to recall that there were other rings besides those (at least magic rings made by the Elves in Eregion). Do you or anyone else has any proof to the contrary, that there could be other lesser rings which didn't have gems in them that could have the similar description as Sauron's ring?

Yes.

Gandalf, from The Shadow of the Past:

"In Eregion long ago many Elven-rings were made, magic rings as you call them, and they were, of course, of various kinds: some more potent and some less. The lesser rings were only essays in the craft before it was full-grown, and to the Elven-smiths they were but trifles - yet still to my mind dangerous for mortals. But the Great Rings, the Rings of Power, they were perilous."

So, there were many rings made, in addition to the 20 that are referred to as the Rings of Power. And the fact that Bilbo's Ring conferred the power of invisibility (and caused him to lie concerning the circumstances of its discovery) did not mean that it could not be a lesser ring, since lesser rings were still powerful as far as mortals are concerned. So I would say that vastly narrows the odds of Bilbo's Ring being the One Ring from 7/1.

The difference is that while Eru can see the events from an outside perspective (being God) he probably knows that the things that will happen there will be readressed at a later time eg. Arda remade.

Surely that makes him all the more incompetent. He could see that much suffering would take place and yet did not take early action to prevent this, despite clearly having the power to do so. Gandalf, however did not have the luxury of seeing things from the "outside perspective". If he had had that luxury, no doubt he would have acted differently.