Short answers, pulled from the story.
The name "Bee Gees" derived from the initials of Brisbane radio presenter Bill Gates, speedway promoter Bill Goode, and Barry Gibb, who first introduced the brothers to Brisbane audiences in 1960. The name was not, as widely believed, a reference to "Brothers Gibb".
The Bee Gees sold an estimated 120 million to 250 million records worldwide, placing them among the best-selling music artists of all time. The Rock and Roll Hall of Fame stated in 1997 that only Elvis Presley, the Beatles, Michael Jackson, Garth Brooks, and Paul McCartney had outsold them at that time.
The Bee Gees won five Grammy Awards for Saturday Night Fever across two years: Album of the Year, Producer of the Year (shared with Albhy Galuten and Karl Richardson), Best Pop Performance by a Duo or Group with Vocals for both "How Deep Is Your Love" and "Stayin' Alive", and Best Vocal Arrangement for Two or More Voices for "Stayin' Alive".
The Bee Gees were inducted into the Rock and Roll Hall of Fame in 1997. The award was presented by Brian Wilson of the Beach Boys, and the group received the honour under the title "Britain's First Family of Harmony".
Robin Gibb quit the group in mid-1969, partly because he believed manager Robert Stigwood was favouring Barry as the frontman, and partly because of a dispute over which side of a single should be the A-side. He felt "Lamplight" should have led the release rather than "First of May". Barry and Maurice briefly continued before also parting ways professionally on the 1st of December 1969.
The Bee Gees wrote the core songs for Saturday Night Fever "virtually in a single weekend" at the Chateau d'Herouville studio in France, after Robert Stigwood commissioned them during post-production on the film. Barry Gibb alone is credited as the only songwriter to have four consecutive US number-one hits, with "Stayin' Alive", "Love Is Thicker Than Water", "Night Fever", and "If I Can't Have You".