separation of Shadowfax and Gandalf

[Gwaihir the Windlord]

I believe I can address each of those questions for you. Starting from the last.

- The life of a mearas was in fact as long as that of a human. Each horse tended to accompany its King until its death.

It was upon Felarof thatEorl rode to the field of Celebrant; for that horse proved as long lived as Men, and so were his descendants.

- In Valinor, I believe, all animals (that have been, are, and are yet to be in the world) are to be found; and as the land is Undying, it is probable that there they are immortal. It is possible that I've got this idea from the Lost Tales or something, but I've got a feeling that it's from the Silm.

Did Shadowfax go with Gandalf to the West? It is probable, if that line of Gandalf's was true. As I should think it was; Shadowfax was to be the last of the mearas's line, a thing that would be explained by his passing into the West.
Perhaps that's where he belonged.

Men said of them that Bema (whome the Eldar call Orome) must have brought their sire from West over sea.

Sort of on loan to Middle-Earth, for a while, they may have been.