Short answers, pulled from the story.
McCartney chose the Höfner 500/1 because it was affordable, costing around thirty pounds at a time when a Fender cost close to a hundred, and because its symmetrical body shape looked less awkward when played left-handed. He placed his order at the Steinway Musikhaus in Hamburg, and the instrument was likely the first left-handed 500/1 Höfner ever built.
The Höfner 500/1 was introduced in 1955, designed by Walter Höfner as an electrically amplified semi-acoustic bass with a hollow body. It was first shown to the public at the Frankfurt Music Fair in early 1956.
McCartney's 1961 Höfner 500/1 was stolen from a van in 1972 and remained missing for over fifty years. The Lost Bass Project, launched in September 2023 by Nick Wass, traced it to someone's attic on the south coast of England, and its recovery was confirmed in February 2024. McCartney played it onstage on the 19th of December 2024 at The O2 Arena in London.
The "Cavern bass" refers to the pre-1962 configuration, where both pickups were mounted close together near the neck heel, giving them a very similar tone. The 1963 model used the 1962 redesign that moved the second pickup toward the bridge, giving each pickup a more distinct character.
The Höfner 500/1 made its last Beatles appearance on the 30th of January 1969, at the Apple Corps rooftop concert. McCartney used his 1963 model at that performance and switched to a Rickenbacker for the recording of Abbey Road shortly after.
Notable Höfner 500/1 players include Tom Hamilton of Aerosmith, who used it on Just Push Play and "What It Takes," Kevin Parker of Tame Impala, Satomi Matsuzaki of Deerhoof, Murray Cook of The Wiggles, Robbie Shakespeare, Jon Anderson on Olias of Sunhillow, and Zach Dawes of The Last Shadow Puppets.