Short answers, pulled from the story.
I Me Mine was written by George Harrison on the night of the 7th of January 1969, after a difficult rehearsal day at Twickenham Film Studios. The melody was drawn from incidental music Harrison heard on the BBC that evening, attributed either to an Austrian brass band on Europa - The Titled and the Untitled or to music by Tristram Cary for Out of the Unknown.
The three pronouns in the title are a conventional reference to the ego in Hindu and Buddhist philosophy. Harrison intended the song as a commentary on egoism, drawing on Swami Vivekananda's teachings and verses 2:71 and 2:72 of the Bhagavad Gita, which advocate a life devoid of egotism and the sense of mineness.
The song had to be formally recorded because footage of the Beatles rehearsing it appeared prominently in the Let It Be documentary film, requiring a studio version for the soundtrack album. The session took place on the 3rd of January 1970 with Harrison, McCartney, and Starr; Lennon had privately left the group in September 1969 and was in Denmark at the time.
Spector extended the track on the 23rd of March 1970 by copying the tape from the one-minute-and-twenty-second mark and repeating the rock chorus and second verse, adding fifty-one seconds to the running time. On the 1st of April he overdubbed a twenty-seven-piece string section, six brass players, and additional drums by Ringo Starr.
The original recording lasted one minute and thirty-four seconds. This version, along with Harrison's mock press statement before take fifteen, was released on the Beatles' 1996 outtakes compilation Anthology 3.
Harrison titled his 1980 autobiography I, Me, Mine after the song, making it the first memoir published by a former Beatle. It was originally issued by Genesis Publications as a luxury leather-bound edition in the style of the same company's Log of HMS Bounty. Harrison wrote in his foreword that the title acknowledged the book could also be seen as a personal ego detour.