and did a state of war remain between it and the USSR post ww2? and if so where there any organized military operations that happened?
The Polish government-in-exile remained in existence until December 1990, when Lech Walesa, the first post-Communist president of Poland, received the symbols of the Polish Republic from the last president of the government-in-exile, Ryszard Kaczorowski.
I can't seem to see anything about organised military operations.