Eldarion would have live at least for 200 years as he was the son Aragorn who also lived for almost 210 years. Eldarion's life expectancy may vary around 200. It would definitely not have been 500 years as that of Elros because Arwen became a mortal woman when she bore King Elessar his son and was no longer an Elf.
In the same text, Tolkien wrote that Eldarion had lived until the age of 125, most likely having passed away in Fo.
No. That was a one-off deal for Elrond's children only. They could be immortal as long as he stayed in Middle-Earth, and if they went with him to Valinor. But if he left and they didn't go with him, they became mortal—period.
Aragorn and Arwen's children would be Mortal--but still long-lived. If Eldarion married an Elf then neither of them would change their essential natures. However, it is conceivable that their children might have the choice of Elven immortality vs. the fate of Men.
Because Aragorn is mortal and Arwen chose to remain in Gondor and become mortal, their son, Eldarion, is mortal as well, despite his Elven lineage.
Elrond has only Half-Elf, and he was once given the choice to be counted among Man or Elves. When he chose to be counted as Elven kind, he was then given immortality. Because Arwen is Elrond's daughter and also Half-Elf, she too has the choice to be a mortal woman or an immortal Elf.
Arwen reciprocated Aragorn's love, and on the mound of Cerin Amroth they committed themselves to marrying each other. In making that choice, Arwen gave up the Elvish immortality available to her as a daughter of Elrond, and agreed to remain in Middle-earth instead of travelling to the Undying Lands.
And after their marriage, both Aragorn and Arwen are mortal. Arwen, therefore, could not set foot in the Undying Lands without special permission. And she wouldn't be likely to go after it in the end. So unfortunately, she would not go there, unlike Legolas, after Aragorn's passing.
At this point Arwen has already given up her immortality, but now she grants the grace of the Eldar to Frodo, not giving him immortality since he is not one of the elves, but instead granting him a home in the undying lands when he does pass.
Arwen didn't want Aragorn to die, because if he died so would she. She said she wasn't tired of living yet. But instead, Aragorn chose to die and Arwen lived a year longer before dying herself.
Originally, Tolkien intended for Éowyn to marry Aragorn. Later, however, he decided against it because Aragorn was "too old and lordly and grim". He considered making Éowyn the twin sister of Éomund, and having her die "to avenge or save Théoden".
Once an elf engages in reciprocated love with someone, that's it. If he cannot be with that person he will lose the will to live, die, and become a forever-shade in the Halls of Mandos. Elves do not move on.
Elrond chooses to be immortal and stay in Lindon as a captain and herald of Gil-Galad, the High King of the Noldor. Once Elros and Elrond separate as do their fates.
Average Elven Lifespan
Elves have the ability to live forever thanks to their immortality. Elves like Elrond, who was over 6000 years old in The Lord of the Rings, are not hard to come by.
Legolas does not marry or have any children, based on the appendix of The Lord of the Rings. Regardless of who his mother was, Legolas is the last of his line. When he sails into the West at the beginning of the Fourth Age, he leaves no family members behind.
She has a vision of a child clothed in white running across her path. She watches as the boy runs with his arms outstretched to his father, an aged Aragorn, who picks him up with joy and kisses him. As the boy looks at her and she sees he is wearing the Evenstar, she knows the boy to be her child.
At the end of The Lord of the Rings, Frodo sets sail for the Undying Lands, which implies that he will live in peace and harmony for all eternity. This is where the immortal Elves come from (most recently) and where they return to when they find that their work in Middle-earth is done.
Legolas is an elf, so he is immortal. However, he is only immortal in the sense that he will never die of old age or sickness. He can die in battle.
So, Elrond had powers not because he was half elven, but because he chose to be counted among the elves and thus retained the power and immortality of the elves.
Arwen was her granddaughter
Galadriel and Celeborn had a daughter named Celebrian, who married Elrond and became the mother of Arwen (as well as her brothers, Elladan and Elrohir).
Eventually, Legolas came to Ithilien with some of his people, with his father's leave, to live out his remaining time in Middle-earth helping to restore the devastatedforests of that war-ravaged land.
When they meet, Arwen is thousands of years old with immortal beauty and he a young 20-something man. However, next time they meet, Aragorn is in his 50s. This was when Arwen fell in love with him, so his 30 years of maturing must have done some good.
Princess Arwen Evenstar gave her beautiful necklace to Aragon to pledge her eternal love to him. This special gift from an immortal elf to a mortal man symbolized Arwen's decision to forsake her immortality to be with the person she truly loves.
Eowyn was left to lead the nation in his stead, as she was brave and beloved by the people. She led the people of Edoras to the White Mountains, where they took shelter. She stayed with them (albeit reluctantly) while the men fought in the Battle of Helms Deep.
In the year 121 of the Fourth Age, after Aragorn's death, Arwen died of a broken heart at Cerin Amroth in Lórien, and was buried there one year after the death of Aragorn, to whom she had been wedded for 122 years. She was 2901 years old.