Short answers, pulled from the story.
The lowest naturally occurring air temperature ever recorded on Earth is -89.2 degrees Celsius, measured at Vostok Station in Antarctica on the 21st of July 1983. Satellite data from 2010 to 2013 identified temperatures as low as -93.2 degrees Celsius along a ridge between Dome A and Dome F, though those readings came from remote sensing rather than a staffed weather station.
The Southern Hemisphere Pole of Cold is located at Vostok Station, a Russian Antarctic research station situated at 3,488 metres above sea level, more than 1,000 kilometres from the nearest sea coast. Temperatures there rarely rise above -25 degrees Celsius in summer and frequently fall below -70 degrees Celsius in winter.
Verkhoyansk and Oymyakon, both in the Sakha region of Russia, compete for the title of Northern Hemisphere Pole of Cold. Verkhoyansk holds the oldest documented record, dating to measurements by Ivan Khudyakov in 1868 and 1869, while Oymyakon recorded -67.7 degrees Celsius on the 6th of February 1933.
The Klinck Automatic Weather Station in Greenland recorded -69.6 degrees Celsius on the 22nd of December 1991. The World Meteorological Organization validated the observation nearly 30 years later and accepted it as the officially lowest near-surface air temperature for the Northern and Western Hemispheres.
Vostok Station sits at a higher elevation than the South Pole and is more than 1,000 kilometres from the nearest sea coast, removing the moderating influence of ocean water. The South Pole is on average 5 to 10 degrees Celsius warmer than Vostok, and its lowest recorded temperature is -82.8 degrees Celsius compared to Vostok's -89.2 degrees Celsius.
Before 1995, Vostok was the only research station on the Antarctic Plateau above 3,000 metres, leaving vast stretches of ice with no instruments. Any temperature colder than -89.2 degrees Celsius occurring in those unmeasured areas would go undetected. Locations like Dome A lacked an automatic weather station until 2005, and satellite measurements taken between 2010 and 2013 later found temperatures as low as -93.2 degrees Celsius along an ice ridge between Dome A and Dome F.