Short answers, pulled from the story.
The battle for the city itself began on the 13th of September 1942, and the German 6th Army finally capitulated on the 2nd of February 1943. This period marked the duration of the major engagement between Axis forces and Soviet troops in southern Russia.
Operation Uranus was launched on the 19th of November 1942 to surround the German forces in the Stalingrad region. The plan involved three complete armies punching through weakly defended flanks to encircle approximately 330,000 Axis personnel.
On the 23rd of August 1942, the Luftwaffe dropped some 1,000 tons of bombs on Stalingrad during the most intense aerial bombardment at that point on the Eastern Front. At least 90% of the city's housing stock was obliterated as a result of this single raid.
Hitler promoted Paulus to Generalfeldmarschall because there was no record of a German or Prussian field marshal having ever surrendered. This promotion implied that if Paulus surrendered, he would shame himself and become the highest-ranking German officer ever to be captured.
Controlling Stalingrad meant gaining access to the oil fields of the Caucasus and having supreme authority over the Volga River transport hub. The city also held significant symbolic importance because it bore the name of Joseph Stalin, the leader of the Soviet Union.