Whaaaat? This Reasoning makes no sense imho.
The linguistic approach is a nice idea, but there is no real clue for that. Usually when Tolkien uses a word in a special context it is capitalized. That way the west (direction) is different from The West (Valinor).
Also as Walk stated Eru does not intervene directly with Arda.
Also is Ea really a nickname for Eru? As the second paragraph states Ea is the name of the existing physical world, because it literally "is".
The Secret Fire reason does not offer any explanation. It doesn't show any connection between Tom and Eru, only states that he contains the Secret Fire. Well yeah, every living being in Arda contains the Secret Fire.
Yes, I agree
Arda, and, more extensively, the physical Universe are something completely separated from Ilúvatar itself, and Tolkien states this clearly by saying that Eru LOVES the Universe and its LOVE makes possible the very Universe's existence as well, rejecting though a sort of 'animistic' vision that determines God as present in every being and substance in the World and the World itself.
Ilúvatar, as the only almighty and omniscient God, has always existed in the past, it always does it in the Present, and forever will be in the Future; the source of everything's existence.
Eru created Eä (the physical Universe) like a 'box' characterised by our common conceptions of Reality, Time, Space and Matter, to make its plan have a concrete and direct realisation in the 'material dimension', determining the 'fundamental rules and boundaries' of the beginning of History.
But, when most of the Ainur entered Eä moved by the Love for it, they discovered that the 'box' was dark and not realised at all, despite what they had been previously shown by Eru in the great Music.
Thus, it was the Valar's duty (with the help of the Maiar) to fill this empty 'box' with their creations and powers.
And this is a very fundamental aspect, because it clearly explains why the World created by the Archangels (neither almighty nor omniscient) was never perfect and often subjected to the marring caused by the Evil, and, indirectly, by the very Valar's mistakes.Eru, apart from very few special exceptions, will remain detached in its Timeless Halls until the End of Time and the final 'Judgement'.
That's why I don't consider at all Tom Bombadil being neither the incarnation of God nor God itself.
And, I also disagree with Ilúvatar and Eä being the same thing; it's wrong, I guess.
I don't remember precisely the quotation, but Tolkien states it clearly: they are two separate 'things'.