This is speculation that, once again, does NOT exist in the trilogy. Compare for example, the Silmarillion, in which the ultimate outcome is the ironic realization that the entire struggle of the elves against Morgoth which had occupied the narrative was a futile struggle doomed to failure, because Morgoth was a Valar and could never be defeated by elves or men. There is similar speculation about the nature of Tom Bombadillo, but ultimately there is no clear answer because the story never tells you who or what he is. Were Saruman and Radagast and Sauron also Maia? The story doesn't say so.
Nor were that the case, would it make the stories any more "Christian." A satanic allegory would certainly include angels and fallen angels.
Yes, yes, and yes.
Yes. According to the essay "Of the Istari," published posthumously in one of the volumes of "Unfinished Tales" (although I know longer recall precisely which one. Gandalf was Olorin (sp?) the Maia, and a favorite of Varda the Queen of the Valar. She arranged for him to be part of the expedition of the Istari (wizards) against his will. He was the only one who remained steadfast in his purpose and was rewarded with permission to return to Valinor. (In RotK we find the spirit of the dead Saruman striving vainly to return as well, but a "cold wind from the west" (obviously sent by the vengeful Valar, or even Eru) disperses him forever.)
However, your point that this is not in the triolgy is well taken.