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I think that Tolkien's "only three unions" really referred to the Pereldar, those who were descended from Edain and Eldar; Mithrellas, as a Silvan Elf, would not have been counted as Eldar.
Or, at least, it's arguable.
Tolkien used the Pereldar wording through much of his drafts, so it's certainly possible that this concept was what (possibly erroneously) survived into print.
On the immortality question - in The Lost Road, as of just before writing The Lord of the Rings, in the final full narrative of Earendil's voyage, the Valar debated what was to be done with him. His Elven blood was raised, but Mandos said something along the lines of "Any mortal blood makes one mortal" (I don't have the books with me). And Manwe sought the advice of Iluvatar and for this case only was given the authority to issue a choice to Earendil and his immediate family. That the Choice was passed to Elladan, Elrohir and Arwen makes things a bit more complicated, but given that the implication from Tolkien's worldview was that accepting the Gift of Death was the "right" choice, it could be argued that this was so that their parents could not withhold the Gift of Eru from them. And once the "right" choice was made, no further choice need be given.
Again, though, much is up to personal interpretation, but that particular interpretation seems coherent to me and forms my personal interpretation.
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