Short answers, pulled from the story.
Paul McCartney wrote the song I've Got a Feeling which emerged from a merger with John Lennon's unfinished track during their 1970 album Let It Be sessions. The final version of the song appeared on the original 1970 album featuring the rooftop performance as its primary recording.
The Beatles performed the merged track I've Got a Feeling on the 30th of January 1969 during their rooftop concert. This live take became the primary version released on the original album while a studio recording made about a week earlier appeared on the Anthology 3 compilation in 1996.
Billy Preston added Fender Rhodes piano to the personnel list for the session of the song I've Got a Feeling. His electric piano sound distinguished the track from other Beatles recordings according to Ian MacDonald who listed Preston as an additional musician alongside the four band members.
Audio isolation techniques enabled a virtual duet between John Lennon and Paul McCartney during the 2022 Got Back tour by isolating Lennon's vocals. Peter Jackson produced his Get Back documentary which allowed McCartney to perform the song live using these separated audio tracks despite their physical separation by decades.
The first recording of John Lennon's contribution to the song I've Got a Feeling happened in early December 1968 at his Kenwood estate. A portable cassette tape captured the performance for later use before the main studio work began.