Short answers, pulled from the story.
The Quarrymen formed in November 1956 with John Lennon, Eric Griffiths on guitars, Pete Shotton on washboard, and Bill Smith on tea-chest bass. This initial lineup was established after Lennon decided to make music following his exposure to Lonnie Donegan records.
Paul McCartney joined The Quarrymen after Ivan Vaughan introduced him to John Lennon at a church fête on the 6th of July 1957. McCartney made his official debut with the band on the 18th of October 1957 at a Conservative Club social held at the New Clubmoor Hall in Norris Green.
The group changed their name from Johnny and the Moondogs to Japage 3 after failing to win a Star Search competition in early 1960. They eventually adopted the name The Beatles by March 1960 after Stuart Sutcliffe joined as a bass player.
The Quarrymen recorded their first session at Phillips Sound Recording Services located at 38 Kensington in Liverpool on the 12th of July 1958. They recorded In Spite of All the Danger followed by Buddy Holly That Be the Day using a single microphone.
The Quarrymen opened the Casbah Coffee Club on the 29th of August 1959 following renovations to Mona Best's cellar. The residency lasted for four months into the new year 1960 until they lost the venue due to a dispute over payments.