Short answers, pulled from the story.
Gerd von Rundstedt commanded Army Group South during the invasion of Poland in September 1939, with Erich von Manstein serving as his chief of staff. Army Group South advanced alongside Army Group North in that campaign.
Army Group South's principal objective during Operation Barbarossa was to capture Soviet Ukraine and its capital, Kiev. The plan called for an advance as far as the Volga River, clearing the way for Army Group North's push toward Leningrad and Army Group Center's push toward Moscow.
Army Group South was split into Army Group A and Army Group B in 1942 to carry out Case Blue, the campaign into southern Russia and the Caucasus. Army Group A was ordered south to capture the Caucasus oil fields.
By the end of December 1943, Army Group South numbered 328,397 German soldiers. Another 109,816 allied and non-German volunteer troops served alongside them.
Army Group South fought in Western Hungary until March 1945, then retreated into Austria as the war in Europe ended. On the 2nd of April 1945, it was renamed Army Group Ostmark and became one of the last major German military formations to surrender to the Allies.
General Friessner commanded Army Group South in October 1944, overseeing the German Sixth Army under General Fretter-Pico and the German Eighth Army under General Wöhler. The Hungarian Second Army under General von Dalnoki and the Hungarian Third Army under General Heszlényi served alongside these German forces.