I think Elves had superior bodies that would not deteriorate in any way, unless they were slain outright.
Only when they were in Valinor, under the blessing of the Valar, where no one and nothing ever decays. Not in Middle-Earth, however. After Elves had lived a long time in Middle-Earth, and once they grew weary of it, their bodies would age, or become slightly "transparent" : this is how Frodo sees Galadriel after they have that lil pic-nic just before they part (i can't give the exact quote now). Another example is Círdan the shipwraight who even had a beard, and hence probably appeared as an old man.
I imagine that they enjoyed eating and drinking. I think they loved fish and game, and whatever plant food they could gather.
They certainly did. There's that nice part in LOTR where Frodo has dinner with Gildor Inglorion. There it already becomes clear that Elvish food and drinks are something very special and cannot be compared to human food : miruvor, lembas, ...
I for me think that Elves are not vegetarians - it is described for instance that some sons of Fëanor were great hunters, and i presume they hunted for animals to eat, not just for fun (killing for fun would not be in the spirit of Elves, even not in the spirit of Caranthir the Dark).