Short answers, pulled from the story.
"I've Got a Feeling" combines Paul McCartney's unfinished song of the same name with John Lennon's unfinished piece "Everybody Had a Hard Year". The two fragments run simultaneously rather than in sequence, with McCartney's verses and Lennon's litany layered together.
The version used on the Let It Be album was recorded on the 30th of January 1969 during the Beatles' rooftop concert. A studio take recorded approximately a week earlier was later released on the Anthology 3 compilation in 1996.
Billy Preston played Fender Rhodes piano on "I've Got a Feeling". He was an additional musician brought into the Let It Be sessions.
"I've Got a Feeling" appears on the Beatles' 1970 album Let It Be. A version also appears on the 2003 remix album Let It Be... Naked, which is a composite edit drawing from two separate rooftop concert performances.
During the production of Peter Jackson's Get Back documentary, Lennon's vocal was isolated from the original recording. McCartney used that isolated vocal to perform "I've Got a Feeling" live on his 2022 Got Back tour, singing his own part while Lennon's voice played through the speakers.
The film is Rape: Film No. 6, an art film by Yoko Ono. It used footage of Lennon performing the song in the back garden of his Kenwood estate and was broadcast on Austrian television on the 31st of March 1969.