"Sindarin (Grey-elven) is properly the name of the languages of the Elvish inhabitants of Beleriand, the later almost drowned land west of the Blue Mountains. Quenya was the language of the Exiled High-Elves returning to Middle-earth.
In the Third Age, the time of the setting of The Lord of the Rings, Quenya was learnt as a second language by all Elves of Noldorin origin, and it continued to be used in spoken and written form, but their mother-tongue was the Sindarin of the Grey-elves.
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.
("A star shines on the hour of our meeting.") Galadriel is perhaps the only major Elf character in The Lord of the Rings that had learned Quenya as a cradle-tongue: she was born in Valinor in the days of the Two Trees.
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."
However, as Elrond (and, of course, Elros) were raised by Maglor, but were born in Middle-Earth, would they speak Sindarin or Quenya? They might have spoken both. Having been born at the Havens of Sirion, they most likely spoke Sindarin as their birth tongue.
As others have noted, 'Galadriel' is a Sindarin name, not a Quenya name. It means 'radiance-crown-girl', or 'maiden crowned with a garland of bright radiance' if you want to be more poetic.
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.
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.
The Numenoreans spoke Adunaic (their language, a language of the Edain) and Sindarin. Their scholars also spoke Quenya. Most people in Numenor spoke Adunaic 1st and also spoke Sindarin.
Gandalf and Saruman here actually speak Quenya, not Sindarin. It's an older form of Elvish, and not spoken as much in Middle-earth. It's kind of like Latin is to us. But here we get some of it, which ties Gandalf and Saruman to a much more ancient time.
There are actually two forms of Elvish commonly learned by fans: Quenya, or high Elvish, and Sindarin, both based loosely on Finnish and Welsh, two languages Tolkien himself studied. And these can be subdivided into different dialects.
An elf knows Elvish because fundamentally, they are fey, and being fey means knowing Elvish. The language evolves as it is needed, and all fey creatures know the language.
Its Sindarin cognate Galadriel was chosen by her to be her Sindarin name, because it was the most beautiful of her names and had been given to her as an epessë by her lover, Teleporno of the Teleri, whom she wedded later in Beleriand.
[ˈkʷwɛɲa]) was one of the languages spoken by the Elves. It was the tongue that developed among those non-Telerin Elves who reached Aman (the High Elves) from an earlier language called Common Eldarin. Quenya was typically written with the Tengwar of Fëanor. An older script, Rúmil's Sarati, was used also.
No, Legolas was a Silvan Elf whereas Galadriel was Noldorin. It is possible that Legolas was related to some of the Elves of Lothlorien, but not to Galadriel.
Character. Although he lived among them, Legolas was not fully of the Silvan Elves. As a son of the Elven-king Thranduil, who had originally come from Doriath, Legolas was at least half Sindar; his mother's identity is completely unknown.
Thingol learns of the Kinslaying at Alqualondë. He bans the speaking of Quenya of Beleriand; the Noldor adopt Sindarin and only speak Quenya in private and in Gondolin.
Arwen means "Noble Maiden" in Sindarin, from ara- ("noble") and gwenn ("maiden"). Tolkien remarked that it also means "greatly blessed" in Welsh. The Quenya form of her name is not entirely certain, but in his Quenya greeting, Aragorn refers to her again as "Arwen" (Arwen vanimelda, namárië!).
