Oh, Indis, thank you so much for that comforting thought: yes, Orome chased them down and then let them go on their way. Definitely! I do believe that the Valar didn't eat as we understand eating, mostly because of sheer numbers. They were these huge beings, the size of a three-story building,, so just imagine how much they would have to eat if they ate like we children of Iluvatar do. But the animals... they would have to eat something, and if one considers the exponential population growth of some species, like mice and such, they would sadly have to be gobbled or else they would overrun even the immense mansion of Aüle.
I remember a book I read years ago, Never Cry Wolf by Farley Mowat the Canadian zoologist. Seeking to provide hard evidence that wolves were not responsible for the loss of deer populations, he took up residence in the neighborhood of a family of wolves and documented their every move for a year and more. In short, it turned out that the wolves ate mice, dozens and dozens of them, that were a plague anyway. Farley himself went on a mouse diet to prove that it was possible to survive on it, and had many more adventures that went into this wonderful book.
Meaning, then, that the big cats and bears and such in Valinor could have maybe preyed on species that require thinning. And that would go for Huan and Manwe's eagles as well. Let's say. The fact is that the balance of Nature went very well for millions of years, until the seeds of Morgoth had their way with Middle Earth, and now so much has been lost.
And Brego, I too believe that Elves would be pretty much vegan or at least moderate consumers of animal-based foods. Honey, most assuredly. Eggs, what can I say... But not all Elves! I can easily see Fëanor and his sons devouring shanks of meat roasted over roaring fires. Or what?
Then again, I don't think Elves were big eaters. That would be why they were so amused by the unquenchable appetites of hobbits.