SANLIURFA, Turkey — When Abu Hamza, a former Syrian rebel, agreed to join the Islamic State, he did so assuming he would become a part of the group’s promised Islamist utopia, which has lured foreign jihadists from around the globe. Instead, he found himself being supervised by an Iraqi emir and receiving orders from shadowy Iraqis... All of the men, however, were former Iraqi officers who had served under Saddam Hussein... His account, and those of others who have lived with or fought against the Islamic State over the past two years, underscore the pervasive role played by members of...