Short answers, pulled from the story.
Gary Gygax created Greyhawk, starting it in 1972 as a dungeon beneath a castle built to entertain his children and friends. It grew closely tied to the earliest development of Dungeons and Dragons.
Castle Greyhawk was first played in 1972, when Gygax's children Ernie and Elise took the roles of Tenser and Ahlissa. In that first session they destroyed monsters Gygax later recalled as either giant centipedes or a nest of scorpions.
Gygax named it the Flanaess because that was the only part of the continent Oerik that fit onto two sheets of paper. His printer's maximum paper size was 34 by 22 inches. He named the region for the Flannae, a peaceful people he imagined had once lived there.
Zagyg was the insane architect Gygax placed at the bottom, thirteenth level of the original Castle Greyhawk dungeons. His name was a reverse homophone joke on Gygax's own name. Only three players ever reached him, Rob Kuntz as Robilar, Ernie Gygax as Tenser, and Terry Kuntz as Terik, each during a solo adventure.
Gygax was forced out of TSR on the 31st of December 1985 after a power struggle within the company. Afterward, TSR shifted its focus to a new setting called Dragonlance, and the World of Greyhawk was never expanded beyond the Flanaess again.
The Greyhawk Wars was a conflict started in 582 CY by the evil half-demon Iuz, spreading until it touched almost every nation in the Flanaess. A peace treaty was signed in the city of Greyhawk two years later. TSR followed the war with a darker boxed set called From the Ashes in 1992.