Short answers, pulled from the story.
Lev Landau received the 1962 Nobel Prize in Physics for his mathematical theory of superfluidity, specifically for explaining the properties of liquid helium II at temperatures below 2.17 Kelvin. He was unable to accept the prize in person because of injuries sustained in a car accident earlier that year.
Landau was arrested on the 27th of April 1938 for possessing a leaflet that compared Stalinism to German Nazism and Italian Fascism. He was held in the NKVD's Lubyanka prison and released on the 29th of April 1939 after Pyotr Kapitsa wrote to Joseph Stalin and personally vouched for Landau's conduct, threatening to resign if Landau was not freed.
The Theoretical Minimum was a comprehensive exam Landau created covering all aspects of theoretical physics, which students had to pass before being admitted to his school. Between 1934 and 1961, only 43 candidates passed it. Those who did went on to become notable theoretical physicists.
Landau maintained a private list ranking physicists on a logarithmic scale from 0 to 5, with 0 assigned to Isaac Newton and 0.5 to Albert Einstein. The founders of quantum mechanics, including Bohr, Dirac, and Heisenberg, received a rank of 1. Landau initially placed himself at 2.5, then later revised his own score to a 2.
The Course of Theoretical Physics is a ten-volume work covering the entire subject of theoretical physics, begun by Landau and his former student Evgeny Lifshitz during Landau's years at the Ukrainian Physics and Technology Institute in Kharkov in the 1930s. The volumes are still widely used as graduate-level physics texts.
Landau died on the 1st of April 1968, aged 60, from complications of injuries sustained when his car collided with an oncoming truck on the 7th of January 1962. The crash had left him in a coma for two months and permanently ended his scientific work. He was buried at the Novodevichy Cemetery.