What happened to Galadriel?

Why are Elladan and Elrohir numbered among the Noldor? Only their grandmother, Idril, was of that kindred (yes, Tuor was eventually numbered among them, as well, but only long after Earendil was born) - the rest were either men, Sindar, or Maia. The Noldorin element is only a small fraction.

I have yet to see any explicit reference in Tolkien's work or notes as to the fate of the brothers. My theory (admittedly baseless) is that they only stuck around until Arwen died, and then returned to Valinor. Nothing supports this, but then there was no reason for them to hang out in Middle Earth any longer, either. If they had become mortal, would they have then been numbered as great lords or kings of Gondor? That does not seem the case, since Aragorn and Arwen produced heirs.

Or perhaps one returned to Valinor and one became mortal, as was the case with Elrond and Elros.

One tangental question: what was the fate of Aragorn's and Arwen's children? Since they were the offspring of man and elf, were they given the same choice as Elrond and Elros? If so, did any of them go to Valinor?

It is all very confusing!