Iraq’s Parliament chose an American-backed former intelligence chief as the new prime minister early Thursday morning, giving the country its first real government in more than five months as it confronts an array of potentially crippling crises. The prime minister, Mustafa al-Kadhimi, 53, who has a reputation for pragmatism, was also seen as an acceptable choice to Iran, the other major foreign power competing for influence in Iraq. Mr. al-Kadhimi is Iraq’s first real prime minister since the last one resigned in November in the face of persistent antigovernment protests. He has already promised to take a new approach to the social unrest, meeting protesters and consulting with them rather than backing the previous government’s sporadic efforts to crush or ignore the turmoil. But the protest movement that arose over government corruption and persistent joblessness last fall is no longer the government’s most pressing crisis. […]