Short answers, pulled from the story.
The song was written by Paul McCartney and is officially credited to Lennon-McCartney. John Lennon himself attributed the idea to McCartney, though Mal Evans and Neil Aspinall also contributed ideas to the concept.
McCartney conceived the idea on a flight back to England from Kenya in November 1966. Roadie Mal Evans asked what the letters "S" and "P" stood for on their in-flight meal trays, and McCartney's explanation of salt and pepper sparked the name and the fictional band concept.
Recording began on the 1st of February 1967 in Abbey Road's studio 2, with George Martin producing and Geoff Emerick engineering. The track was completed on the 6th of March 1967 after three additional sessions.
The Beatles never performed the song live during their touring years. Three former members, McCartney, Harrison, and Starr, along with Eric Clapton, played it at Clapton's wedding party on the 19th of May 1979.
Jimi Hendrix performed the song live at the Saville Theatre in Shaftesbury Avenue just three days after the record was released in 1967, with McCartney and Harrison in the audience. The theatre was leased by Brian Epstein.
The charity single released after McCartney and U2 performed the song at Live 8 on the 2nd of July 2005 set a world record for the fastest-selling online song of all time. It reached number 1 on the UK Downloads chart and number 48 on the Billboard Hot 100.