Short answers, pulled from the story.
Tolkien drew from multiple medieval sources including the Old English poem Beowulf, the Middle English romances Sir Gawain and the Green Knight and Sir Orfeo, Icelandic folklore collected by Jón Árnason, and Norse mythology's division between Light Elves and Dark Elves. Scholar Tom Shippey identifies the Middle English lay Sir Orfeo as the key "fusion or kindling-point" of Tolkien's thinking.
Tolkien created two primary Elvish languages: Quenya, originally called "Elfin" or "Qenya", which became High-elven; and Sindarin, the Grey-elven tongue. Both are described as the most complete of his constructed languages. The Elves in his fiction are also credited with inventing two writing scripts: the Tengwar, attributed to Fëanor, and the Cirth, attributed to Daeron.
According to Marjorie Burns, Tolkien eventually but hesitantly chose elf over fairy. By 1915 the word fairy had accumulated many contradictory associations, and John Garth supposes Tolkien was warned against it partly due to its growing association with homosexuality. Tolkien acknowledged in his 1939 essay On Fairy-Stories that both words had been shaped by French, Germanic, Scandinavian, and Celtic influences.
Tolkien's Elves are immortal and do not die of disease or old age, though they can be killed in battle. When they die, their souls travel to the Halls of Mandos in Valinor, where after a period of rest their spirits are clothed in bodies identical to their old ones. Elves who remain too long in Middle-earth eventually undergo a process of fading, in which their immortal spirits overwhelm their bodies, making them invisible to mortal eyes.
Elves marry freely, monogamously, and only once in their lives. Betrothal involves an exchange of rings lasting at least a year, and the wedding ceremony consists of words spoken by bride and groom that include the name of Eru Ilúvatar, followed by a feast. Elvish pregnancies last about a year, Elves reach full physical maturity between their fiftieth and one hundredth year, and they have few children with long intervals between them.
Tolkien-style Elves became a staple of fantasy literature and role-playing games from the 1960s onwards. In role-playing games such as Dungeons and Dragons they appeared as standard non-human characters, typically portrayed as skilled archers, mentally sharp, lovers of nature and music, and gifted in magic. Peter Jackson's Lord of the Rings film trilogy, released between 2001 and 2003, further spread a particular visual interpretation of the Elves drawn partly from the Celtic Revival tradition.