Short answers, pulled from the story.
The tour ran from the 2nd of February 1963 to the 3rd of March 1963. It was split into two parts, with the Beatles playing independent dates between the 12th and the 22nd of February before rejoining Helen Shapiro's tour on the 23rd.
The Beatles were fourth on an eleven-act bill headed by Helen Shapiro. Shapiro was 16 years old at the time and closed each show as the headline act.
The tour was organised by the Arthur Howes Agency. It was the first time the Beatles had worked with Howes.
The Beatles' typical set included "Chains" (sung by George Harrison), "Keep Your Hands Off My Baby" (John Lennon), "A Taste of Honey" (Paul McCartney), and "Please Please Me" (Lennon and McCartney). "Love Me Do" and "Beautiful Dreamer" were kept as prepared alternatives.
On the 11th of February 1963, between the two parts of the tour, the Beatles recorded ten tracks in a single day. Those recordings, combined with their two previously released singles, formed their debut album, Please Please Me.
Yes. John Lennon and Paul McCartney wrote "From Me to You" while travelling to Shrewsbury on the 28th of February 1963, during the second leg of the tour. It became the next Beatles single after the tour ended.