Short answers, pulled from the story.
The Soviet Union invaded eastern Poland on the 17th of September 1939, seventeen days after Germany began its invasion from the west. The borders were formally finalized in the German-Soviet Frontier Treaty signed on the 28th of September 1939.
The Molotov-Ribbentrop Pact was a non-aggression agreement signed by the Soviet Union and Nazi Germany on the 24th of August 1939. A secret protocol divided Eastern Europe into spheres of influence, assigning eastern Poland to the Soviet Union. This protocol was not publicly revealed until after Germany's defeat in 1945.
The Soviet Union annexed territories totaling 201,015 square kilometers with a population of approximately 13.299 million. Some 21,275 square kilometers near Bialystok and Przemysl were later returned to Poland, and the permanently annexed areas held roughly 10.653 million people according to the 1931 census.
The Katyn massacre was the execution of Polish prisoners of war ordered by the Soviet Politburo, including Stalin, on the 5th of March 1940. NKVD officers selected victims from camps and prisons in occupied western Ukraine and Belarus, and approximately 22,000 people were killed.
The Soviet regime deported 1.45 million people from eastern Poland between 1939 and 1941, of whom 63.1% were Poles and 7.4% were Jews. Polish historians, drawing on Soviet archives, estimate total Polish deaths at the hands of the Soviets at around 350,000 for the period 1939-1945.
Most of the eastern Polish territories were permanently incorporated into the Ukrainian and Byelorussian Soviet Socialist Republics. The formal cession was signed on the 16th of August 1945. Poland was compensated with German eastern territories, but its total land area shrank by roughly 77,000 square kilometers.