Galadriel is a Sindarin name translated by Tolkien as "maiden crowned with a garland of bright radiance", "Maiden crowned with gleaming hair", "glittering garland", and "maiden crowned with a radiant garland". Galadriel consists of galad ("light, radiance") + rî ("crown").
Her name "Ar-wen" means 'noble maiden' in Sindarin. She was given the name "Evenstar" as the most beautiful of the last generation of High Elves in Middle-earth. Arwen said: "Dark is the Shadow, and yet my heart rejoices; for you, Estel, shall be among the great whose valour will destroy it."
Consequently, Elrond was descended from all three tribes of the Elves (Vanyar and Noldor through Idril, Sindar through Lúthien), a Maia, and all three houses of the Edain (Hador, Haleth and Bëor).
As an elf of Mirkwood, Legolas speaks Silvan, or least knows some words and phrases. Finally, he definitely speaks Sindarin, which is the most common elvish language at the time of the quest to destroy the One Ring.
Galadriel is one of the Calaquendi, meaning "Elves of the Light" in Quenya. Some of the earliest Elves to come into existence, the Calaquendi dwelt in Valinor with the gods during the halcyon Years of the Trees, which predate even the First Age of Middle-earth.
Galadriel was perhaps the only known High Elf in Middle-earth during that time who (having being born in Valinor) had learned Quenya as a cradle-tongue. The poem Namárië is the longest piece of Quenya found in The Lord of the Rings. It is also known as Galadriel's Lament.
Which one should learn first? This question can't be answered directly: it largely depends on what languages you're already familiar with. I believe that Quenya is appropriate for the starter because it gives better understanding of the Primitive language, and then he can find Sindarin easier.
Now then the most often asked question of “which should I learn?” This is often followed closely by “Which language is easier?” To start, neither language is really “easier” than the other. Quenya is easy for some while others find that Sindarin is easiest for them.
Sindar (meaning "Grey People" [note1]) or Grey Elves were Elves of Telerin descent who inhabited Beleriand. They were united under Elu Thingol, the King of Doriath, and later his grandson Dior Eluchíl.
Voice. Gandalf, known temporarily as the Grey and later the White, and originally named Olórin (Quenya), was an Istar (Wizard), dispatched to Middle-earth in the Third Age to combat the threat of Sauron.
The name Morgoth is Sindarin (one of Tolkien's invented languages) and means "Dark Enemy" or "Black Foe". Bauglir is also Sindarin, meaning "Tyrant" or "Oppressor". "Morgoth Bauglir" is thus an epithet.
Of these two groups of Elves, most of the Noldor returned to Middle-earth where they met the Sindarin-speaking Grey-elves. The Noldor eventually adopted Sindarin and used Quenya primarily as a ritual or poetic language, whereas the Vanyar who stayed behind in Eldamar retained the use of Quenya.
Rivendell ("cloven-dell") is the Common Speech translation of the Sindarin name Imladris ("deep dale of the cleft"). An alternative (or complementary) etymology, gives Rivendell as the Anglicised version of the Westron name Karningul (itself a translation of Imladris).
Originally the three Keepers were Gil-galad, Galadriel, and Círdan. Gil-galad gave his Ring to Elrond and Círdan gave his to Gandalf. At the end of the Third Age, when the Rings finally lost their power and were taken into the West, the Keepers were Elrond, Galadriel and Gandalf.
In "The Lord of the Rings," Arwen spoke to Frodo and Sam in the language of her people, the Elves. Specifically, she conversed with them in Sindarin, one of the Elven languages.
The languages were the first thing Tolkien created for his mythos, starting with what he originally called "Qenya", the first primitive form of Elvish. This was later called Quenya (High-elven) and is one of the two most complete of Tolkien's languages (the other being Sindarin, or Grey-elven).
Aragorn son of arathorn was raised by Elrond of Rivendell, he was taken there as a baby, and was likely taught how to hunt, shoot, fight, and speak elvish, but he could of learned the other traits from the wild. He could of been taught by Elrond or by elvish tutors, if those exist.
It perhaps isn't "neccessary", but Aragorn lived in Rivendell from when he was 2 to around 20, so he would have grown up being taught both languages equally (his mother teaching him the common tongue, the elves teaching him Sindarin).
Narya (the Ring of Fire, the Red Ring), from Quenya nár, "fire", was set with a ruby. Its metal is not stated. It gave its wielder resistance to the weariness of time, and evoked hope and courage in others. Its final bearer was the Wizard Gandalf, who received it from Círdan at the Grey Havens during the Third Age.
Who is Legolas? 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.
The TL;DR version: First, she's a Half-Elf. She is descended from two marriages of Man and Elf, through her father Elrond. Second, as far as her Elven ancestry she's a little bit of everything, but mostly mixed Noldor/Sindar, with some Vanyar. The Longer version: Arwen Undómiel is what is called a Peredhel, a Half-Elf.
