Short answers, pulled from the story.
The Service for Poland's Victory was established on the 27th of September 1939 by General Michał Karaszewicz-Tokarzewski. This initial group evolved into the Home Army on the 14th of February 1942 under orders from General Władysław Sikorski.
Membership swelled to approximately 200,000 soldiers by early 1943 and ranged between 200,000 and 600,000 people by mid-1944. Only about 5 to 10 percent were armed at any given time due to severe weapon shortages.
Polish sources provided 48 percent of all reports received by British secret services from continental Europe between 1939 and 1945. The network employed over 1,600 registered agents who gathered information including detailed drawings of V-2 rocket systems.
The largest battle known as the Warsaw Uprising started on the 1st of August 1944 and lasted until the 2nd of October 1944. Polish forces controlled substantial parts of the capital city but received no aid from the approaching Red Army.
The Home Army officially disbanded on the 19th of January 1945 after the Red Army cleared most Polish territory of German forces. This decision aimed to prevent civil war and armed conflict with their former allies who now viewed them as obstacles to communist control.