Short answers, pulled from the story.
Decca chose to sign Brian Poole and the Tremeloes instead because they were local and would require lower travel expenses. The label's executives also told Brian Epstein that guitar groups were on the way out and that the Beatles had no future in show business.
The audition took place on the 1st of January 1962 at Decca Studios in West Hampstead, north London. The session was formally called a commercial test and ran from the morning into the afternoon.
The Beatles recorded fifteen songs at the Decca audition, far exceeding the standard procedure of two to five songs. Epstein chose the setlist, which included three Lennon-McCartney originals and twelve covers.
Five songs from the Decca audition were officially released on the compilation album Anthology 1 in 1995: "Searchin'", "Three Cool Cats", "The Sheik of Araby", "Like Dreamers Do", and "Hello Little Girl".
The decision to reject the Beatles is disputed. Most accounts point to either Dick Rowe or Mike Smith. Epstein attributed the famous "guitar groups are on the way out" quote to Dick Rowe in his 1964 autobiography A Cellarful of Noise, but Rowe denied making that remark for the rest of his life.
George Martin, a producer at EMI's Parlophone subsidiary, heard the Decca demos and decided he wanted to meet the band. That meeting led to the Beatles signing with Parlophone after every EMI producer Epstein had previously approached declined.