Short answers, pulled from the story.
George Harrison, then a member of the Beatles, founded Harrisongs in 1964. He first registered the company as Mornyork Ltd on the 11th of September 1964, and it had been renamed Harrisongs Ltd by the 7th of December that same year.
Harrisongs is headquartered at 27 Ovington Square in London's Knightsbridge district. The same building houses the Beatles' company Apple Corps.
Harrison was dissatisfied with the royalties and status he received from Northern Songs, the company Dick James and Brian Epstein set up in 1963 for John Lennon and Paul McCartney. In 1967 he wrote "Only a Northern Song" about that frustration, then let his Northern Songs contract expire in March 1968 and began publishing through Harrisongs.
Harrisongs publishes Harrison's compositions from 1968 onward, including "Sour Milk Sea", four songs on the Beatles' self-titled double album such as "While My Guitar Gently Weeps", and two songs from Abbey Road, "Here Comes the Sun" and "Something". It also published his solo work, including All Things Must Pass and Living in the Material World.
The catalogue from 1974's Dark Horse onward is now published by Umlaut Corporation, which is controlled by Harrison's widow, Olivia Harrison. As of 2016, the wider Harrisongs catalogue has been administered worldwide by the Bicycle Music Company, a division of Concord Music.
Yes, Harrisongs is also the publishing company for thenewno2, the indie rock band led by Harrison's son Dhani. That portion of the catalogue is administered by BMG Rights Management.