Immortality

[Voralphion]

Elwing had an elven mother, Luthien and a human father, Beren.

This is incorrect. Elwing was in fact the daughter of Dior, the son of Luthien and Beren. Elwing had a half elven father, Dior, and a full elven mother, (sorry I can't remember her name).
Also, Luthien only gave up her immortality so that Beren could return from the dead. She made this deal with the Valar only after she had already died from grief at the losing of Beren. She was granted that wish only because the song that she sang in the Halls of Mandos was so sad that even Mandos took pity on her.