Short answers, pulled from the story.
The Beatles performed All You Need Is Love live on the 25th of June 1967 as part of Our World, the first live global television link. The broadcast reached an audience of over 400 million viewers in 25 countries.
All You Need Is Love was written by John Lennon and credited to the Lennon-McCartney partnership. McCartney recalled in the 1990s Beatles Anthology interviews that the song was essentially entirely Lennon's, with contributions from the other Beatles confined to ad-libs at the end.
All You Need Is Love reached number 1 in the UK, where it held the top of the Record Retailer chart for three weeks after entering at number 2. It also topped the Billboard Hot 100 in the US for one week and reached number 1 in many other countries. The Recording Industry Association of America certified it Gold on the 11th of September 1967.
The song opens with bars from the French national anthem La Marseillaise and ends with a long coda that incorporates Glenn Miller's 1939 hit In the Mood, Greensleeves, Bach's Invention No. 8 in F major (BWV 779), the Prince of Denmark's March, She Loves You, and Yesterday. George Martin placed some quotations deliberately; the She Loves You and Yesterday excerpts came from Lennon improvising during rehearsals.
The studio guests at the Our World broadcast on the 25th of June 1967 included Mick Jagger, Keith Richards, Eric Clapton, Keith Moon, Graham Nash, Marianne Faithfull, and Pattie Boyd. Also present were Mike McGear and Jane Asher, McCartney's brother and girlfriend respectively, along with members of the Small Faces and the design collective the Fool.
All You Need Is Love became the anthem of the 1967 Summer of Love and has remained a touchstone for expressions of universal harmony. Bob Geldof cited the Beatles' Our World performance as inspiration for Live Aid in 1985. A handwritten copy of the lyrics sold at auction in 2005 for $1.25 million. Global Beatles Day, held each year on the 25th of June, was established in 2009 to commemorate the original broadcast.