Short answers, pulled from the story.
Ernest Shackleton died at 2:50 a.m. on the 5th of January 1922, of a fatal heart attack, while his ship Quest was moored at South Georgia. At his wife Emily's request, he was buried in the Grytviken cemetery on South Georgia on the 5th of March 1922.
Shackleton's most famous exploit was the open-boat voyage of the James Caird, a 720-nautical-mile journey across the southern ocean from Elephant Island to South Georgia in 1916, after his ship Endurance sank in the Weddell Sea. He and five companions made the crossing in a 20-foot lifeboat, then crossed 32 miles of South Georgia's mountains on foot to reach the Stromness whaling station.
On the 9th of January 1909, Shackleton and three companions reached a Farthest South latitude of 88 degrees 23 minutes S, just 112 statute miles from the South Pole. This was the largest single advance toward the Pole in exploration history at that time.
Shackleton was sent home from the Discovery Expedition in 1903 on health grounds after collapsing during the southern journey. Captain Robert Falcon Scott wrote that he "ought not to risk further hardships in his present state of health", though some contemporaries later alleged that Scott's true motive was resentment of Shackleton's popularity with the crew.
Endurance became trapped in pack ice in the Weddell Sea on the 19th of January 1915, drifted northward for months under ice pressure, and sank on the 21st of November 1915 at position 69 degrees 5 minutes S, 51 degrees 30 minutes W. The wreck was discovered just over a century after Shackleton's death.
Shackleton is remembered as a model leader for extreme circumstances, particularly for his ability to keep his crew alive and unified after the loss of Endurance. Sir Raymond Priestley summarised this reputation in his 1956 address to the British Science Association: "When disaster strikes and all hope is gone, get down on your knees and pray for Shackleton." Management writers, the US Navy, and universities including the University of Exeter have used his approach as a study in people-centred leadership.