Short answers, pulled from the story.
John Lennon wrote the verses after attending an all-night festival at London's Alexandra Palace on the 29th of April 1967. Paul McCartney later added a chorus to this unfinished piece in July 1967.
The Beatles recorded the track during a six-hour session starting at 9 pm on the 11th of May at Olympic Sound Studios in Barnes south-west London. This marked the first Beatles EMI recording created entirely outside EMI Studios according to author Mark Lewisohn.
Baby You're a Rich Man appeared as the B-side of their All You Need Is Love single released on the 7th of July in the United Kingdom and the 17th of July in the United States.
The group required twelve takes before achieving a satisfactory rhythm track due to various disruptions during the session. Engineers Keith Grant and Eddie Kramer assisted producer George Martin during the process.
Parts of the song were used in their 1968 animated film Yellow Submarine appearing towards end when Sgt Pepper's Lonely Hearts Club Band released from paralysis initiated by Blue Meanies hatred of music. The Beatles recording also played at end of 2010 film The Social Network about rise of Facebook and co-founder Mark Zuckerberg.