Short answers, pulled from the story.
The recordings were made during the Beatles' final Hamburg residency in late December 1962, most likely across several sessions between Christmas and New Year's Day. The commonly cited date for the last session is the 31st of December 1962, the group's last day in Hamburg.
Stage manager Adrian Barber used a Grundig home reel-to-reel recorder set to 3 and three-quarter inches per second, with a single microphone placed in front of the stage. The low-fidelity result means vocals sound muffled and some songs were initially misidentified on early releases.
By December 1962, the Beatles were gaining popularity in Britain and had just achieved their first charted single with "Love Me Do". They had booked the Star-Club engagement months in advance, before their British profile had risen.
Paul Murphy formed Lingasong specifically to release the recordings after acquiring the tapes. The Beatles failed in a legal attempt to block the 1977 release. They eventually won full ownership of the recordings in a 1998 court ruling, with George Harrison's in-person testimony cited as a key factor.
When Pickwick Records released its 1979 reissue, it included a track called "Hully Gully" mistakenly credited to the Beatles. It was actually performed by Cliff Bennett and the Rebel Rousers, another act on the Star-Club bill.
Film director Peter Jackson confirmed in 2023 that he and his staff had located and purchased the original tapes, with plans to use machine learning to improve their sound quality. However, Apple had no release plans at the time of that announcement.