Short answers, pulled from the story.
The Afrika Korps was formed on the 11th of January 1941. Erwin Rommel was confirmed as its commander on the 11th of February 1941, after Hitler rejected the original choice, Hans von Funck.
Germany dispatched the Afrika Korps as a blocking force to support Italian forces in Libya after the Italian 10th Army was destroyed and captured by the British Commonwealth Western Desert Force in Operation Compass and at the Battle of Beda Fomm in early 1941.
The Afrika Korps surrendered on the 13th of May 1943, along with all remaining Axis forces in North Africa. Most prisoners of war were transported to the United States and held at camps including Camp Shelby in Mississippi and Camp Hearne in Texas.
Erwin Rommel was known as "the Desert Fox" (der Wustenfuchs). The nickname reflected his reputation as one of the most capable tank commanders of the war, demonstrated during the North African campaign.
The historical record is contested. Robert Satloff documented that Afrika Korps soldiers plundered Jewish property along the Libyan coast during the retreat. Deportations of Jews to the concentration camp at Giado in Libya were carried out under the period of German-Italian control, and shootings of Jews in Benghazi were recorded. Some historians, including Gershom Gorenberg, assign primary blame for civilian persecution to Italian colonial authorities rather than to Rommel's corps directly.
The force underwent multiple reorganizations between 1941 and 1943. The parent formation was redesignated from Panzer Group Africa to Panzer Army Africa on the 30th of January 1942, and later to the German-Italian Panzer Army and then Army Group Africa. The term Afrikakorps was the official name for fewer than six months, though troops used it throughout the campaign's full 27 months.