[Raynor]

That said, if Gandalf wasn't incumbered by the mandate and allowed to manifest as the Maia Olorin, would he have been as powerful as Sauron? Powerful enough to take him on one-on-one?

The original five maiars were said to be "mighty, peers of Sauron", cf The Istari, Unfinished Tales.

For that matter, was anyone fully aware that the wizards were also Maiar?

I doubt that; Gandalf himself was considered by Men just an elf, cf the same source above.

That said, if Sauron had reclaimed the ring/regained all of his power, could the Valar have still personally unseated him if they'd gotten super-****ed (as they did with Morgoth).

I doubt that:

Originally Posted by RotK, the last debate

If he regains it, your valour is vain, and his victory will be swift and complete: so complete that none can foresee the end of it while this world lasts.(Gandalf)

But you can always bet on euchatastrophe in Tolkien's world .

Is it feasible to suggest that perhaps one of his lieutenants--Sauron in all likelihood--might have tried to overthrow him;

I wouldn't say so:

Originally Posted by Myths Transformed

Melkor was not Sauron. We speak of him being 'weakened, shrunken, reduced'; but this is in comparison with the great Valar. He had been a being of immense potency and life.

and more to the point:

While Morgoth still stood, Sauron did not seek his own supremacy, but worked and schemed for another, desiring the triumph of Melkor, whom in the beginning he had adored.

(and even in RotK, Sauron is named "servant of Morgoth").

was Ungoliant more powerful than Morgoth?

At the time they confronted each other, Melkor was weakened and he transfered a lot of his power to Ungoliant, who also sucked dry the Two Trees, the wells of Varda and absorbed the power of many noldor artefacts; we don't even know if she could have actually kill him. In "normal" conditions, Ungoliant would lose, imo.