Short answers, pulled from the story.
Józef Wybicki wrote the lyrics between the 16th and the 19th of July in 1797. He composed the text while working inside Reggio Emilia in Northern Italy following the Third Partition of Poland.
The melody is a lively mazurka derived from folk dances of Mazovia in central Poland. No single composer created the original tune though Kazimierz Sikorski later developed a modern harmonization used today.
The fourth stanza mentioning Russians disappeared after the signing of a Franco-Russian alliance at Tilsit in 1807. The final stanza referring to Kościuszko vanished because he refused to support Napoleon's war in Poland.
Poland's constitution defines this anthem as one of three state symbols alongside the coat of arms and national colors. Men must uncover their heads during public performances and uniformed services perform a two-finger salute if not in organized groups.
Samo Tomášik wrote the Slovak ethnic anthem Hej Sloveni based on the slowed melody of this song. Ukraine drew inspiration from the lyrics of Poland Is Not Yet Lost for its own national anthem while Yugoslavia adopted it before splitting into Serbia and Montenegro after 2006.