Tolkien vocabulary I (serious)

[The Squatter of Amon Rûdh]

My personal view is that JRRT used that style of language for two reasons: He wanted to write in an authentic epic prose style and he liked that sort of language anyway. Few people of his time were better qualified to use it.
Incidentally, puissant is Norman French, what one might call the official language of knighthood in England (knighthood itself being a forcibly imported concept). The word occurs quite often in the Morte D'Arthur, in which we find a later retelling of Gawain and the Green Knight. I don't know whence 'Fey' comes, but they used to call fairies "the fey folk" and sometimes it can be used to describe someone with perceived supernatural abilities as well as a recklessly fatalistic mood. It can generally be considered to imply a certain other-worldliness, as in the name Morgan le Fay, which uses a corrupted form.