OK, Great! Trivia Quiz

Answer: Ieri Oggi Domani

In "Ieri, Oggi, Domani" ("Yesterday, Today, Tomorrow", 1963) Sophia Loren played three different women from different social classes, and Mastroianni played the three romantic interests of these three women. The three characters coincide with three different stories that are not intertwined.
De Sica (1901-1974) was the first director to create four Best Foreign Movies, all of which are listed in the question.
The very first Best Foreign Movie was "Sciuscia" (1946), known in English as "Shoeshine". In this movie De Sica portrayed two young boys near Rome trying to gain a living by polishing shoes, just after the Second World War. The main roles were for Franco Interlenghi and Rinaldo Smordoni.
De Sica's first major international success was "Ladri di Biciclette" (1948, "Bicycle Thieves") with Lamberto Maggiorani and Enzo Staiola in the main roles. Maggiorani played Antonio Ricci, whose bike was stolen. Antonio and his son (played by Enzo Staiola) tried to track down the thief, but without evidence they did not obtain justice.
"Il giardino di Finzi Contini" (1970, "The Garden of the Finzi-Continis") told about a wealthy Jewish family in the 1930s, as the historic horror approached. The main roles were played by Lino Capolicchio and Dominique Sanda.

Answer: René Clement

René Clement (1913-1996) was the first French director to create several Best Foreign Movies. "Au delà des grilles" (1949, "The Walls of Malapaga") and "Jeux Interdits" (1952, "Forbidden Games") both won the honorary award, and Clement was also nominated for his 1955 movie "Gervaise".
"Jeux Interdits" was set in France occupied by Hitler's troops, and told about a very young orphan girl named Paulette (played by Brigitte Fossey, aged six) residing with another family. Paulette and the young teen Michel tried to cope with death of their beloved family members by performing funeral rituals on deceased animals.
René Clair, Eric Rohmer and Henri-Georges Clouzot may have directed movies of which I would say "Oh, Great", but they did not win the title of Best Foreign Movie. I'll mention their nominated movies: "Porte des Lilas" (1956, René Clair), « La Vérité » (1959, Clouzot) and « Ma nuit chez Maud » (1968, Eric Rohmer).  

Answer: Toshiro Mifune

Toshiro Mifune (1920-1997) starred in many of Kurosawa's great movies. In "Rashomon" he played the bandit accused of killing a samurai. The same story was told from the viewpoints of many of those involved (the bandit, the samurai's wife, a woodcutter who found the body, and even the deceased samurai himself through the intercession of a spiritual medium).
Mifune also played in Kurosawa's great movies "Seven Samurai" (1954), "Throne of Blood" (1957) and "Yojimbo" (1960).
Kurosawa also won the Best Foreign Movie for the Soviet Union, with "Dersu Uzala" (1975).
Ando (born 1975) starred in "Battle Royale" (2000). Masahira Kobayashi (born 1971) starred in "Godzilla, Mothra and King Ghidorah: Giant Monsters All-Out Attack" (2001). Ken Watanabe (born 1959) played in "Letters from Iwo Jima" (2006). All these were born after Kurosawa's "oh great" movie "Rashomon". 

Answer: Federico Fellini

Fellini (1920-1993) was one of the greatest Italian directors. He directed the Best Foreign Movie four times: later he also won for "Otto e Mezzo" (1962) and "Amarcord" (1973).
"La Strada" (1954) with Anthony Quinn and Giulieta Masina told about a couple working in a travelling circus. In "Le Notte di Cabiria" (1957) Masina played a prostitute roaming Rome, hoping to find true love.
Gavaldon was a Mexican director, nominated for "Macario" (1960). Cacoyannis was Greek and directed (among others) "Electra" (1962) and "Iphigenia" (1977). Bardem was a Spanish director, nominated for "Venganza" (1957, "Vengeance"). 

Answer: Marcel Camus

Marcel Camus (1912-1982) was the one we were looking for. As far as I found, he was no relative of the author Albert Camus. "Orpheu Negro" (1959) was based upon the Greek myth about Orpheus, the talented musician, and his beloved Eurydice - whom he set out to bring back from the underworld. But the movie transposed the action to the Carnival in Rio de Janeiro, with interesting twists.
Marcel Camus also directed the war comedy "Atlantic Wall" (1970) with Bourvil.
The other were also French directors who won the aforesaid Oscar.
Cloche won Best Foreign Movie with "Monsieur Vincent" (1947). Bourguignon directed "Les dimanches de Ville d'Avray" (1962, « Sundays and Cybele »). And Wargnier won with « Indochine » (1992).
 

Answer: Mon oncle

All these French movies won the Oscar for Best Foreign Movie. However, "Mon Oncle" was the only movie by (and with) Jacques Tati.
Tati (1907-1982) is best known for his typical comedies such as "Les vacances de Monsieur Hulot" (1953), "Mon oncle" (1958), "Play Time" (1967) and "Trafic" (1971). In all these movies he played the character of Monsieur Hulot: an aging man who can't cope with modern society.
In "Mon oncle" Monsiuer Hulot visited his brother-in-law: an industrial pioneer who equipped his house with all modern gadgets.
Claude Lelouch directed "Un homme et une femme » (1966). François Truffaut made «La nuit américaine » (1973). And « Préparez vos mouchoirs » (1978, « Get Your Handkerchiefs Ready ») was a comedy by Bertrand Blier.

Answer: The Seventh Seal

A knight (played by Max von Sydow) challenged Death himself for a game of chess in "Det sjunde inseglet" ("The Seventh Seal", 1957). If Death would win, the knight would succumb to the Plague. Although this was in my opinion one of the greatest Ingmar Bergman movies, it wasn't even nominated for Best Foreign Movie.
"Jungfrukällan" ("The Virgin Spring", 1960), "Sasom en I spegel" ("Through a Glass Darkly", 1961) and "Fanny och Alexander" (1982) did win the Oscar.

Answer: War and Peace

"Vojna I Mir" ("War and Peace", 1966) by Sergei Bondarchuk is a movie that one shouldn't try out when in a hurry. Total playing time is a whopping 7 hours and 7 minutes, and even this is only a condensed version of Tolstoy's novel. Bondarchuk himself played the role of Prince Pierre Bezukhov, who started as a fan of Napoleon - until the French army invaded Russia. Kirill Lavrov and Ivan Pyryev directed the Russian version of "The Brothers Karamazov" in 1969, based upon a novel by Fyodor Dostoyevsky. "Amadeus" (1984) directed by Milos Forman was based upon Peter Shaffer's transposition of Pushkin's short story "Mozart I Salieri". Vladimir Petrov directed "Revizor" (1952) based upon a story by Nikolai Gogol.

Answer: Anti-Semitism

"Obchod na korze", as the original Slovak title goes, told the story of Antonin Brtko, a Czech carpenter with Aryan roots, and Rozalia Lautmannova, a Jewish owner of a shop for needle and threads, at the start of the 1940s. German occupation troops imposed various anti-Semitic measures, one of them being the transfer of business ownership from Jews to designated Aryans. The main characters were played by Ida Kaminska (Rozalia) and Jozef Kroner (Antonin).
Jan Kadar (born Janos Kadar) had Jewish ancestors himself.

Answer: Z

"Z" by Costa-Gavras was the movie we're looking for. In a country that is not specified, the opposition led by the character known as Z (role by Yves Montand) held a peace rally, but a wild driver steered into the crowd and fatally injured Z. The other one-letter titles are also movie titles made outside of the USA. "V" (2005) was directed by an Australian (James McTeigue) with an English-Australian (Hugo Weaving) and an Israeli protagonist (Natalie Portman). "M" (1931) was directed by a German (Fritz Lang) and starred a Hungarian (Peter Lorre) and a Swiss actress (Ellen Widmann). "R" was a Danish movie directed by Tobias Lindholm with Pilou Asbaek as the protagonist.  

Answer: Black and White in Color

"Black and White in Color" was not randomly chosen as the USA title to this movie: it was also the literal translation of the working title. At a final stage the French title was changed to "La victoire en chantant", but many titles outside of the French speaking world were based upon the working title.
Jean-Jacques Annaud directed this movie for Ivory Coast, starring Jean Carmet and Catherine Rouvel. The story was set in the French colonies in Africa during the First World War. Some of the colonists provided the indigenous population with army clothing and with rifles, and convinced them to fight against the Germans in neighbouring countries.
"Friendly Fire" (2006) was a fantasy on the themes of Sean Lennon's music. Sean (son of John Lennon) starred with Asia Argento.
"Little Big Man" (1970) starred Dustin Hoffman as a hundred-year old survivor reminiscing the Battle at Little Big Horn.
"Living Death" (2006) was a movie directed by Erin Berry. Kristy Swanson played a masochist married to the rich and cynical character Victor (role by Greg Bryk).

Answer: Volker Schlondorff

Volker Schlondorff (born 1939) was one of the most successful directors in the German "Neue Welle", which also included great movie makers as Werner Herzog, Rainer Werner Fassbinder and Margarethe von Trotta.
Schlondorff's "Die Blechtrommel" related the story of Oskar Atzenrath, a boy born in 1924 who stopped growing aged three - either because of a curious accident or because he didn't want to grow up in Nazi society.
Wolfgang Becker directed "Good Bye Lenin" (2003), about a young man trying to convince his senile mother that the communist regime in East Germany is still strong.
Oliver Hirschbiegel created the well-known masterpiece "Der Untergang", about the last days of Adolf Hitler (brilliantly played by Bruno Ganz).
Leni Riefenstahl is best known for her documentaries "Olympia" (1938) and "Triumph des Willen" (1935). But besides these movies abused as Nazi propaganda, she also directed "Impressionen unter Wasser" (2002). 

Answer: Krzysztof Kieslowski

Kieslowski (1941-96) was one of the most influential Polish directors, known for the trilogy "Trois Couleurs" - three stories somehow linked to the colours of the French flag and to the ideals of the French Revolution (Liberté, Egalité, Fraternité - translated as liberty, equality and fraternity).
Kieslowski also directed the serial "Dekalog": ten TV movies of one hour each, inspired by the ten commandments.
Pawel Pawlikoski (born 1957) was the first Polish winner of the Oscar for Best Foreign Movie, with his production "Ida" (2014).
Andrzej Wajda (1926-2016) was nominated several times, for "The Maids of Wilko" (1979) and "Man of Iron" (1981).
Agnieszka Holland (born 1948) was nominated for "In Darkness" (2011).

Answer: Bunuel won the Oscar for Best Foreign Movie with a French movie

Luis Bunuel (1900-1983) was indeed one of the great Spanish directors, but many of his movies were French productions. Bunuel started his career with one of his masterpieces: the short movie "Un chien andalou" (1929), best known for the dream sequence inspired by Salvador Dali. "Belle de jour" (1969) with Catherine Deneuve was another of his great French movies. But he did win the Oscar for Best Foreign Movie with "Le charme discret de la bourgeoisie" (1972), in which six upper-middle-class friends try in vain to organize a dinner party.

Answer: Amour

Michael Haneke was born in 1942 in Munich (Germany) but was raised in Austria, where his maternal family lived. He started his career with some TV movies ("After Liverpool", 1974, followed by "Drei Wege zum See" and "Sperrmull", both from 1976). In 1989 his first theatrical movie was completed ("Der Siebente Kontinent"). International fame came with "Funny Games" (1997, remade in 2007 with an American crew), followed by "La pianiste" (2001).
Haneke received an Oscar for "Amour" (2012), a movie about love at old age. Jean-Louis Trintignant and Emmanuelle Riva played a couple well in their eighties, of whom the wife suffered a stroke and got paralyzed as a result.
"Happy End" (2017) was another typical Haneke production: a title that promises light entertainment, but with darker themes - in this case the fugitive camps near Calais, and the decline of a bourgeois family.