Short answers, pulled from the story.
A flight controller monitors technical aspects of a mission using telemetry from computer consoles. Each controller serves as an expert in one specific area while communicating with remote experts to support frontroom operations.
Guidance officer Steve Bales decided whether it was safe to land or abort the mission when program alarms 1202 and 1201 triggered during the descent of the Lunar Module Eagle. He trusted guidance backroom experts like Jack Garman to determine if the computer overload could be ignored.
Control of U.S. spaceflights moved to the Johnson Space Center in the early 1960s. After this transfer each CAPCOM used the radio call sign Houston for all communication with astronauts.
Global mission control facilities include Baikonur Cosmodrome in Kazakhstan for Roscosmos, Beijing Aerospace Command and Control Center in China, and Tsukuba Space Center in Japan for JAXA. European Space Agency operates from Darmstadt Germany and Kourou French Guiana while Canadian Space Agency manages robotics from Longueuil Quebec.
Flight controllers accept responsibility for operations without support teams most of the time today and make life-or-death choices during critical moments. They must always be aware that they might suddenly find themselves in roles with final outcomes affecting human lives.