Short answers, pulled from the story.
The Beatles' partnership was formally dissolved on the 9th of January 1975 in London, when all four members signed "the Beatles Agreement" in December 1974. Paul McCartney's public press release on the 10th of April 1970 triggered widespread media reports of the split, but the legal dissolution was not finalised until 1975.
The break-up is attributed to multiple factors: the death of manager Brian Epstein in 1967, tensions over McCartney's leadership, John Lennon's heroin use and relationship with Yoko Ono, George Harrison's growing frustration as a songwriter, the mismanagement of Apple Corps, and disputes over the appointment of Allen Klein as business manager.
Allen Klein was the founder of ABKCO Records who became the Beatles' business manager in 1969 after being endorsed by Lennon, Harrison and Starr over McCartney's preferred representatives, the Eastman family. Rob Sheffield described Klein as arguably "the one who played the biggest role in their demise." Klein was eventually dropped by the other three Beatles in March 1973, and a settlement with Apple was reached in January 1977 for $5,009,200.
Lennon privately told McCartney, Starr and Klein at a meeting at Apple on the 20th of September 1969 that he wanted a "divorce," with Harrison absent from that meeting. He kept the departure private at Klein and McCartney's request until McCartney's own public press release on the 9th of April 1970.
The final session at which all four Beatles recorded together was the 20th of August 1969 at EMI Studios, for "The End" on Abbey Road, along with mixing for "I Want You (She's So Heavy)." Their final meeting with all four present was two days later at a photo session at Lennon's Tittenhurst estate.
The four never performed or recorded together after the break-up. Three ex-Beatles appeared on Starr's 1973 album Ringo and on Harrison's "All Those Years Ago" in 1981. In 1994, the surviving three completed Lennon demos "Free as a Bird" and "Real Love" for the Anthology project; "Now and Then" was finished and released in 2023 by McCartney and Starr.