Actually, IIRC, the Valar learned Quenya from the Eldar.
So far as I know. It's also possible I suppose that Quenya evolved a bit in Valinor, but again, there is the issue of how or why, because it's one or two generations! Even if they learned Quenya in Valinor, that was Finwe who learned, and then his kids, Feanor & Fingolfin and their own children who returned to Middle Earth, where they encountered Dad/Grandpa's old pal Elwe, who now goes by Elu Thingol and speaks a whole new language and bans theirs. Why did Finwe (and presumably Olwe & Ingwe, whose kinswomen married Finwe and his youngest son) totally learn a new tongue? Why did Elwe/Thingol and his wife, Melian, a Maia from Valinor, teach their daughter and allow their people to speak, an entirely different language that is unrecognizable as his birth speech or hers? Either Quenya is the original Elven tongue (and it seems to mean "Speech" as the original Elvish name for themselves is "Quendi" meaning 'those who speak' or something like that; so why would they make up a new language and call that "speech", like its the only one. It's like those isolated populations whose name for themselves means "people" or "humans". But if they found a second group of people and named THEM "people". "Speech" is an acceptable name for your only language. It makes no sense as one you develop later), in which case why did Thingol change, or it's got Valinor origins, in which case why did Melian change?

But it's a bit later, I think. Like maybe after the Wars, some of them push east to explore or find new homes. Their place of origin was way east of the Misty Mountains, because that was the point at which the first group of Teleri under Lengwe, the Nandor, bailed. Then there is Eriador, between the Misty & Blue Mountains, and then Beleriand. There isn't even any mention of contact between the Laiquendi (led by Denethor, Lengwe's son) and the original Nandor.
I wasn't sure about that, not knowing much about languages, but I didn't think they were.

Yeah that's true.