The recently popularized version of the "Turkish Revelry" ( = "Golden Vanity/Willow Tree") sung on the double CD of pirate songs issued in connection with Johnny Depp's Pirates of the Caribbean -- sung by Loudon Wainwright III-- stems from Paul Clayton's version, "The Turkish Revelee," recorded in 1957 on his most popular album, Whaling and Sailing Songs from the Days of Moby Dick, Tradition 1005. The record has been reissued on CD at least twice and last time I looked was still available.

Clayton's notes on the song say "The ballad probably originated about the middle of the 17th century when the Barbary pirates (known as Turks) raided shipping in the English Channel and even looted coastal towns." He transcribed and learned his version from a 1932 aluminum recording of one of the best American traditional singers, Horton Barker of Chilhowie / St. Clair's Bottom, Virginia, in the collection of the Virginia Folklore Society. Barker's repertoire contained many of the finest American versions of the Child Ballads. The song was included in a book Clayton made primary contributions to as a graduate student, Arthur Kyle Davis' More Traditional Ballads of Virginia, UNC Press, Chapel Hill, 1960.

I don't know how far back you want to go toward the fountainhead. For the ultimate sources of the ballad, of course, see Francis James Child's excellent-as-always background notes in The English and Scottish Popular Ballads, where he traces it through three clusters of versions in the Pepys Ballads, Logan's Pedlar's Pack and other sources.

He puts the song in the 17th century, and was apparently unable to find earlier traces. The attribution of one version as "Sir Walter Raleigh Sailing in the Low-lands, etc." (which, to answer another of your questions, was a broadside) is almost certainly fantasy about this popular naval hero of a previous era. Child's two other cited versions are, he believes, traditional variants of the original broadside.

By contrast to some other Child ballads involving at least semi-historical sea incidents (like "Captain Ward and the Rainbow"), no firm historical background could be found by Child, that very knowledgeable student of ballad origins, and no specific historical incident is identified.

As to composition, as with most ballads of its age, it is anonymous. It's always worthwhile to try to look for authors in these circumstances, but rarely can one be pinned down. Broadsides in particular were anonymous productions, the tabloid TV of their day.

Bob