By and large I agree Iarwain, and welcome to the Downs Tuor.
However, I would nitpick the following:
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it seems to me that within M-E, Arda, Ea, etc. Eru is both omnipotent and omniscient, and existence as a whole is within his sphere of influence
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Eru is not or perhaps it would be better to say that He rarely exercises omnipotence over the freewill of his children.
I rather imagine you already agree with this but I just wanted to underscore it.