Short answers, pulled from the story.
Army Group B (Heeresgruppe B) was the name given to four distinct German army group commands during World War II. The four formations operated at different times between 1939 and 1945 across Western Europe, the Eastern Front, northern Italy, and the Western Front.
Generalfeldmarschall Maximilian von Weichs commanded Army Group B during its second deployment, which included the advance toward Stalingrad. He held command from the 15th of July 1942 until the 10th of July 1943, overseeing the formation during Operation Uranus and the encirclement of the German 6th Army.
Army Group B was trapped in the Ruhr pocket in northern Germany and progressively divided into smaller sections. The final section surrendered to the Allies on the 21st of April 1945. Commander Generalfeldmarschall Walter Model committed suicide on the same day.
Yes. Erwin Rommel commanded Army Group B from the 10th of July 1943 through to the 17th of July 1944, covering deployments in northern Italy and then in German-occupied France ahead of the Allied Normandy landings.
The fourth Army Group B, under Generalfeldmarschall Walter Model, oversaw the German Ardennes Offensive, known to the Allies as the Battle of the Bulge. At that point the army group held the center of the Western Front, positioned between Army Group H to the north and Army Group G to the south.
The first Army Group B was renamed Army Group Center on the 22nd of June 1941, the very day Germany launched Operation Barbarossa against the Soviet Union. The formation had previously been redeployed from France to East Prussia and the General Government in German-occupied Poland starting in August 1940.