Edain/Eldar marriages

[Legolas]

I came to the part where it explains the three unions of the Edain and the Eldar: Luthien and Beren; Idril and Tuor; and Arwen and Aragorn. When I read this I was curious why it would say only three. Unless I am mistaken there are four, they left out Nimloth and Dior. Nimloth was clearly an elf with Celeborn as her uncle, unless her mother was a human, (which is never even implied,) and she is clearly said to be an Elf-maiden of Doriath. And Dior is a half-elf being the son of Beren and Luthien.
If you can spread some more light on this subject for me I would be grateful.

Dior was a half-elf and Nimloth was an elf. What's your confusion? Those listed are the unification of a man and one of elven blood.

Tuor was a man, Idril was an elf.
Beren was a man, Luthien was an elf.
Aragorn was a man, Arwen was a half-elf.

Those are listed because one half of the relationship was a man. Dior was a half elf, and though he had mortal blood, was not wholly mortal.

(Aragorn had a very small bit of Elven blood, but so small an amount was totally insignificant as to his fundamental kind.)

I also have one question on the marriage of Idril and Tuor. Since Tuor and Idril sailed off into the sunset, and their deaths were never recorded, did Idril sacrifice her immortality for Tuor? I think she would have to since Luthien and Arwen both did also, but I don't remember actually ever reading it through-out all the books.

No elf can just give up their immortality freely - only Eru can give that choice. Tuor was granted immortality by Eru.