Short answers, pulled from the story.
Tarkovsky directed seven feature films: Ivan's Childhood (1962), Andrei Rublev (1966), Solaris (1972), Mirror (1975), Stalker (1979), Nostalghia (1983), and The Sacrifice (1986). He also directed three short films during his studies at VGIK, a stage production of Hamlet in Moscow, and the opera Boris Godunov at the Royal Opera House in London.
Tarkovsky died of lung cancer at Clinique Hartmann in Neuilly-sur-Seine near Paris on the 29th of December 1986. His wife Larisa and actor Anatoly Solonitsyn died from the same type of cancer. Sound designer Vladimir Sharun believed all three died from exposure to chemicals released by a plant upstream from the locations used during the filming of Stalker.
Sculpting in time is the filmmaking theory Tarkovsky developed and named after cinema's unique capacity to alter the viewer's experience of time. By using long takes and few cuts, he aimed to convey a sense of time passing and time lost. He published a book by that title with the University of Texas Press in 1986, the year he died.
Tarkovsky left the Soviet Union in 1979 and formally announced his defection at a press conference in Milan on the 10th of July 1984, stating that returning home would leave him unemployed. Soviet authorities had repeatedly suppressed or restricted his films, and they lobbied at Cannes to prevent Nostalghia from winning the Palme d'Or. He was processed as a Soviet defector on the 28th of August 1985 at a refugee camp in Latina, Italy.
Tarkovsky won the FIPRESCI prize three times, the Prize of the Ecumenical Jury three times (more than any other director), and the Grand Prix Speciel du Jury twice at Cannes. He was also nominated for the Palme d'Or three times and won the Best Director award once. He was too ill to attend the ceremony when The Sacrifice received its prizes, and his son collected the awards on his behalf.
In 1972, Tarkovsky told film historian Leonid Kozlov his ten favorites: Diary of a Country Priest and Mouchette by Robert Bresson; Winter Light, Wild Strawberries, and Persona by Ingmar Bergman; Nazarin by Luis Bunuel; City Lights by Charlie Chaplin; Ugetsu by Kenji Mizoguchi; Seven Samurai by Akira Kurosawa; and Woman in the Dunes by Hiroshi Teshigahara. The list contained no Soviet films and only one film from the silent era.