[Legolas]

Elrian is right. Luthien was half-elven, as was Dior Eluchíl, Elwing, and Eärendil. The choice was not granted until Elros and Elrond, and is not mentioned further than Elladan, Elrohir, and Arwen.

Long before, Luthien elf married Beren man and chose to be a mortal. Does anyone know how long their children lived?

Dior, their only son, was born around 470 FA and slain around 510 FA when the sons of Fëanor attacked Doriath. This premature death leaves us hanging on his fate.

Elrond i[s] called Half-elf in the book, yes, but he once was allowed a chice, Mortal or elven, and he chose Elven. So in my opinion Arwen is 100% elf.

Your opinion in the matter doesn't amount to anything in matters that Tolkien explicitly addressed. Tolkien said she was not to be counted as an elf (nor Elrond, nor any of his descendents). They simply shared the fate of men/elves, but were not men/elves.

Letter No. 154:

The Half-elven, such as Elrond and Arwen, can choose to which kind and fate they shall belong: choose once and for all.

More plainly, in Letter No. 345:

Arwen was not an elf, but one of the half-elven who abandoned her elvish rights.

She was not an elf who turned mortal. She was not considered an elf until she made the choice - she was a half-elf that chose the fate of men over the fate of elves.

Actually, it's strange, that the elves, due to their love, were always allowed to become mortals, like Lúthien, and therefore they were given more changes than Men, who were mortals and could not become anything else.

Ilúvatar and the valar didn't care very much about the Men, it seems

Only Luthien was allowed to do that, and probably only due to her great deeds. On the other hand, Tuor, a man, was granted immortality for service to Ulmo. That makes the score even. Also, Manwë stated that immortality was not his to give, so the Valar cannot make the offer. Immortality was granted by Eru alone. See the quote from Letter No. 153 below for Tolkien's musings on this.

About Aragorn/Arwen's daughters and Eldarion, nothing points toward them having the choice. The choice of the half-elven certainly could not go on forever in accordance with what Tolkien wrote about Eru and the Valar, mortality and immortality, and elves and men (Letter No. 153):

Immortality and Mortality being the special gifts of God to the Eruhini (in whose conception and creation the Valar had no part at all) it must be assumed that no alteration of their fundamental kind could be effected by the Valar even in one case: the cases of Lúthien (and Túor) and the position of their descendants was a direct act of God. The entering into Men of the Elven-strain is indeed represented as part of a Divine Plan for the ennoblement of the Human Race, from the beginning destined to replace the Elves.

From the Appendix A of Return of the King:

To him therefore was granted the same grace as to those of the High Elves that still lingered in Middle-earth: that when weary at last of the mortal lands they could take ship from the Grey Havens and pass into the Uttermost West; and this grace continued after the change of the world. But to the children of Elrond a choice was also appointed: to pass with him from the circles of the world; or if they remained, to become mortal and die in Middle-earth.

Once Elros chose mortality, the rest of his line followed with no say in the matter, and nothing else implies that the generations after Elladan, Elrohir, and Arwen would either. The quote from the appendix says only the children of Elrond and nothing of their children, so we are not to infer that they have the choice. Until told otherwise by author, we should only take in what was written. Had the choice been handed down beyond this generation, he would've said so.

About their privelege to delay the choice - they could only delay it for an indefinite amount of time after Elrond's parting. It does seem a bit unfair, but that's how Tolkien decided it should be.

A little removed from the point of discussion, but interesting still (to me anyway) is the half-elven ancestry:

I have written it out here. (That link is broken now...I don't know how it was deleted.)

It is not possible to determine their exact proportions of race since certain Elven maids' origins are not given (Elenwë, Olwë/Eärwen's unnamed wife/mother, Elmo's unnamed wife, Galadhon's unnamed wife, and Fingoflin's unnamed wife). As it stands with my assumptions that these maids were 100% elven (as whatever kindred they are mentioned as), Arwen, Elladan, and Elrohir were 2/64 Maia, 12/64 Man, 34/64 Sindar, 11/64 Noldor, 5/64 Vanyar [50/64 Elven, 52/64 Immortal]. Arwen's make-up is thus 0.78125 elven.