Regarding Eru and his "thoughts"/the Ainur
Wording wise, they are offspring of Eru's thought, thus Eru's thoughts given life. They can do nothing that Eru himself does not permit, not even Melkor, with Eru saying ""
"There was Eru, the One, who in Arda is called Ilúvatar; and he made first the Ainur, the Holy Ones, that were the offspring of his thought, and they were with him before aught else was made." - The Silmarillion: AINULINDALË
"In the beginning Eru, the One, who in the Elvish tongue is named Ilúvatar, made the Ainur of his thought..." - The Silmarillion: VALAQUENTA
"Manwë and Melkor were brethren in the thought of Ilúvatar." - The Silmarillion: VALAQUENTA
Note: This quote is just a literal example of the Ainur as offspring of Eru's thought. As Eru thought the two as siblings, they thus are.
Moreover, other writings imply that, while the Ainur are "independent beings" with a free will, they are in many ways also extensions of Eru's mind. However, this is less certain.
"But it is also used more vaguely of things arising in the mind or entering the mind (sanar) which the Eldar regarded as sometimes the result of deep reflection (often proceeding in sleep) and sometimes of actual messages or influences on the mind – from other minds, including the greater minds of the Valar and so indirectly from Eru." - Nature of Middle-Earth: Notes on Órë
That's pretty much what I was trying to make clear. The universe Eru created in Low 2-C, and said universe is sustained in his thoughts. Hence a 4d creation is sustained/created as thought