Short answers, pulled from the story.
Yoko Ono conceived the name Plastic Ono Band in 1967 as an idea for an art exhibition in Berlin. John Lennon and Yoko Ono established a romantic relationship by 1968 and began collaborating on musical projects under this name.
John Lennon and Yoko Ono married on the 20th of March 1969 and hosted their first Bed-in for Peace event that same day. Recordings made around this time were released as Wedding Album which contained tracks from their peace advocacy period.
Give Peace a Chance and Remember Love were recorded during the second bed-in held in Montreal in late May and early June 1969. These tracks were released on the 4th of July as a single credited to the Plastic Ono Band and marked the first single released by Lennon outside of the Beatles.
The first performing lineup included bassist Klaus Voormann and drummer Alan White who filled out the group after Eric Clapton replaced George Harrison. The recording of the show at the Toronto Rock and Roll Revival festival was released in December 1969.
John Lennon/Plastic Ono Band and Yoko Ono/Plastic Ono Band were both released on the 11th of December 1970 following sessions in London. The core backing included Klaus Voormann on bass and Ringo Starr on drums while Phil Spector co-produced Lennon's record.
Yoko Ono revived the Plastic Ono Band name in 2009 with the EP Don't Stop Me! which previewed the album Between My Head and the Sky. Core members included Sean Lennon Cornelius Keigo Oyamada and Yuka Honda while the band performed live concerts into 2015.