Short answers, pulled from the story.
Their booking agent Allan Williams sent them after another group he managed, Derry and the Seniors, proved successful there. Williams booked the Beatles into Bruno Koschmider's Indra club starting on the 12th of August 1960, though he admitted he was not impressed with them and hoped to find a better act to follow them.
During their first residency the Beatles slept in a storeroom at the Bambi Kino cinema at 33 Paul-Roosen-Strasse, next to the ladies' toilet. The room had concrete walls, no heat, and bunk beds covered with Union Jack flags. They were paid £2.50 each per day.
Harrison was deported on the 21st of November 1960 because he was 17 years old and therefore too young under German law to work in a nightclub after midnight. Bruno Koschmider, their original club owner, tipped off the police after the Beatles broke their contract with him to move to the Top Ten Club.
The first released Beatles recording was the single "My Bonnie", made in Hamburg with Tony Sheridan as a backing group for West German Polydor Records. It was released on the 31st of October 1961 in West Germany under the name "Tony Sheridan and the Beat Brothers", and in the UK on the 5th of January 1962.
Astrid Kirchherr was a Hamburg fan, then 22 years old, who first heard the Beatles at the Kaiserkeller with friends Klaus Voormann and Jurgen Vollmer. She became engaged to Stuart Sutcliffe in November 1960, is widely credited with inspiring the Beatles' moptop haircut, and was with Sutcliffe in the ambulance when he died of a brain haemorrhage on the 10th of April 1962.
Sutcliffe left the Beatles in 1961 to study art at the Hamburg College of Art under the artist Eduardo Paolozzi, and to remain with Kirchherr. After suffering blackouts and intense headaches, he was taken to hospital on the 10th of April 1962 and died of a brain haemorrhage before the ambulance reached the hospital. He was less than a year out of the band.