Elrond
Elrond was born in the latter part of the First Age. He and his twin brother Elros were both Half-Elven, like each of their parents. It means that they were born of mixed blood; their parentage was half Edain (of the Fathers of Men) and Eldarin (or Elven).
Another character that's incredibly deep is Elrond. In The Lord of the Rings, he was a regal Elf Lord, and his wisdom and power were legendary.
Thus, for Elrond, he gets 25% Elf and 25% Man from his father Earendil's side. So in Elrond, he inherits 25% Elf from father's side plus 31.25% from mother's side, total of 56.25% Elf in him.
Elrond is Half-elven in The Rings of Power and wider Lord of the Rings lore because both of his parents, Eärendil and Elwing, were also Half-elves. In the case of Elrond's father, Eärendil, he had an Elf mother, Idril, and a human father, Tuor.
Legolas is a Sindarin Elf from the Woodland Realm of Northern Mirkwood. His father, Thranduil, is the King of the Silvan Elves living in that realm, making Legolas the Prince of Mirkwood.
She was a royal Elf of both the Noldor and the Teleri, being a grandchild of both King Finwë and King Olwë.
This means that Thranduil had a stronger claim to kingship, and that although both Elrond and Galadriel could have claimed this title too, they both decided against it and were happy to be labeled guardians and protectors of their lands, rather than authoritarian rulers.
Arwen is one of the half-elven who lived during the Third Age; her father was Elrond half-elven, lord of the Elvish sanctuary of Rivendell, while her mother was the Elf Celebrian, daughter of the Elf-queen Galadriel, ruler of Lothlórien.
That choice also extended to their direct descendants. They had two sons, Elrond and Elros. Elrond made the choice to remain immortal among the elves. Elros, however, chose to become mortal instead.
Aragorn is not half Elf, although he is a descendant of Elros, who is half Elf (and the brother of Elrond, the half-Elf who raised him), which explains why Aragorn's life span is unusually long.
Elrond (Robert Aramayo)
Here, he takes on another iconic role: Elrond, the future leader of Rivendell. When The Rings of Power begins, the young Elrond is not yet an elf lord. Instead, he's an ambitious young politician of half-elven heritage.
The Inverse Analysis — In Tolkien's legendarium, the Three Elven Rings of Power are eventually given to Galadriel, Gil-galad (Benjamin Walker), and Círdan the Shipwright.
While Hugo Weaving's Elrond looks a bit older than his peers, this is mostly to show the paternal relationship he has with Arwen (Liv Tyler). Galadriel is actually older than Elrond, but Cate Blanchett is depicted with an angelic presence that gives her eternal youth.
Elrond's ring, Vilya with its blue sapphire, was actually originally given to King Gil-galad. Soon after Elrond became Lord of Rivendell, he inherited the ring from Gil-galad. While Elrond was already a skilled magical healer, receiving this ring of power enhanced his healing abilities dramatically.
Whos older, Galadriel, or Elrond? The version of Galadriel in Morgoth's Ring was said to have been born in 1362 of the Years of the Trees, before the Sun and Moon were made. By contrast, The War of the Jewels cites Elrond's birth as taking place in the year 532 of the First Age.
Arwen isn't necessarily dying because of the Ring, but now that she is mortal, she is dying through the slow decaying of time. Arwen also faces the same fate as all those in Middle Earth should the Ring Bearer fail his mission. So in that way, her fate is tied to the Ring.
Galadriel is of the Noldor, and her mother was of the highest race, the Vanyar; Celeborn was a Sindaran elf from Doriath, so between the two, the rulers of Lórien have the most impressive bloodlines.
"Frodo saw her whom few mortals had yet seen; Arwen, daughter of Elrond, in whom it was said that the likeness of Lúthien had come on earth again; and she was called Undómiel, for she was the Evenstar of her people." Arwen Undómiel, often called Arwen Evenstar, was one of the half-elven, married to Aragorn II.
There is probably no blood relationship. Elrond is of higher birth--he is descended from two of the three ambassadors of the Eldar who were taken by the Valar to see the Two Trees in their glory, and who afterward became Kings (Finwe King of the Noldor and Elwe aka Elu Thingol, King of the Sindar).
So when she allows this incredible rarity to Gimli, she essentially gives him the three hairs that Feanor demanded of her, because she has looked into his soul and found that he has a good heart and that he desires them for nothing more than to treasure the beautiful days he spent in her lands.
Her intentions would have been pure as she sought to instill peace. Ultimately, though, she would have been corrupted, and her beauty would become an object of worship. Thus, Galadriel's dark form in Peter Jackson's trilogy personified what would have happened if had she given into temptation and took it for herself.
Celeborn is known as one of the wisest elves to ever live and he is an especially benevolent ruler. He is also Galadriel's supportive husband.