Halfelvens..

[Mandos]

Why are Elrond, Elros, and Earendil the only ones calles halfelven? There were many others

[Inoldonil]

There weren't really, many others I mean. Dior (son of Beren and Luthien) was the first of the Halfelves, he was called that. 'Perelda' or 'Halfelf' seems exclusively to refer to one of an Elf and a Man, for Luthien is not called one, even though her mother was a Maia and her father an Elf. This might be explained by saying (as it is true) Melian took on the form of an Elf, and the Maiar do not have natural bodies themselves.

The Prince of Dol Amroth only had Elvish blood at long remove, and we don't meet his ancestor that must have been one (a Halfelf).

Eldarion, son of Aragorn and Arwen, was one (if Dior was), but we don't meet him in any literary story.

So there really were only a handful of the Pereldar in history.

[Captain Stern]

Did Dior qualify as a Half Elf?

Luthien returned from the Halls of Mandos a mortal human. Then she and Beren had Dior so I suppose that makes Dior a human.

I don't know?

[Elsilar]

It seemed that after Luthien returned from Valinor her body remained the same. Her fate was "sundered" from the elves and there for became subeject to the gift/doom of men. Her power as a Maia/elf some what remaind because after she returned as a mortal : "Luthien went to Menegroth and healed the winter of Thingol with the touch of her hand."
Here Maia/elveness was passed on to Dior. This is made know when "Dior arose, and about his neck clasped the Nauglamir; and now he appeared as the fairest o fall the children of the world, of threefold race: of the Edain, and of the Eldar, and of the Maiar of the Blessed Realm."
If he were merely mortal then wearing one of the Silmarils would have lessened his countenance whereas for Luthien who was mortal it hastened her end.

[Inoldonil]

Exactly Elsilar.

Anyway as I said, Dior is called the first of the Pereldar (Halfelves).