Short answers, pulled from the story.
The European Theatre of World War II opened with the German invasion of Poland on Friday the 1st of September 1939. On the 6th of October, following the Polish defeat at the Battle of Kock, German and Soviet forces gained full control over Poland.
Polish casualties were about 66,000 dead and 694,000 captured during the campaign that lasted about a month. The success of the invasion marked the end of the Second Polish Republic though Poland never formally surrendered.
Poland was the only German-occupied country to establish an organization specifically to aid Jews known by the cryptonym Żegota. It provided food, shelter, medical care, money, and false documents to Jews despite death penalties for helpers.
Three mathematician-cryptologists Marian Rejewski, Henryk Zygalski and Jerzy Różycki developed techniques to decrypt messages produced on the German Enigma cipher machine from late December 1932 to the outbreak of World War II. They disclosed their achievements to France and the United Kingdom on the 25th of July 1939 near Pyry in the Kabaty Woods south of Warsaw.
The Polish 303 Fighter Squadron claimed the highest number of kills of any Allied squadron during the Battle of Britain. A total of 145 Polish pilots defended British skies including those fighting in British squadrons alongside the four Polish squadrons that took part in the battle.