What is the division of a group into opposing factions, like the Christian church in 1054, called?

A dismembered hand clutching a broken sword is part of which 1937 black-and-white painting inspired by the bombing of a… Latin American countries long complained that Europe's quotas and tariffs on which fruit were discriminatory? Which nation, with its capital at Dili, gained independence from Indonesia in 2002? Which opera diva was nicknamed "Bubbles"? Which word means both a division of a play and the setting where it takes place? Which actor played DJ Dr. Johnny Fever on "WKRP in Cincinnati" and later headed the class on "Head of the Class"? Which word means both a docked horse's tail and a short haircut for women popular in the 1920s? What is a doctor who specializes in the care of the elderly called?