Short answers, pulled from the story.
The Adventures of Tom Bombadil first appeared as a stand-alone book in 1962. J.R.R. Tolkien's own letters confirm that 1962 is the accurate year of release despite some later editions stating 1961.
J.R.R. Tolkien wrote all the poems in The Adventures of Tom Bombadil though several are attributed to Hobbit authors or traditions within the text. Bilbo Baggins is credited with writing Errantry and The Man in the Moon Stayed Up Too Late while Sam Gamgee recites The Stone Troll and Oliphaunt.
Tom Bombadil appears as a character encountered by Frodo Baggins in The Lord of the Rings and was named for a Dutch doll owned by Tolkien's children. The Sea-Bell originally called Firiel before its publication in 1934 recounts a journey to a strange land beyond the sea.
Christina Scull and Wayne G. Hammond edited a new stand-alone edition of The Adventures of Tom Bombadil in 2014 featuring detailed commentary for each poem. They also included original versions and their sources alongside the final texts.
Seven of the works from The Adventures of Tom Bombadil appear on the 1967 album titled Poems and Songs of Middle Earth. Six of these tracks are read by J.R.R. Tolkien himself while the seventh track Errantry is set to music by Donald Swann.