Well, I don't recall ever hearing that Gandalf's return was intended by Tolkien to reflect the Resurrection. Gandalf did not sacrifice himself for the remission of sin: he did it because he was the only one in Moria capable of facing the Balrog. He was sent back because his task was not complete: the overthrow of Sauron, which only he was capable of effectively organizing.
As for the Elves representing angels, the 'angels' in the world were the Valar and the Maia. The Elves were not forced to remain in mortal lands. During the time of LOTR they could pass to the Blessed Realm at any time they chose.Therefore their sadness and longing for the Immortal Shores was self-induced.
As for the parallels between the Ainulindalë and creation, I certainly see them. Whether they were intentional or not I don't know if Tolkien explicitly said.
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Music alone proves the existence of God.
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