Short answers, pulled from the story.
The battle took place from the 13th of August to the 5th of September 1942. The main attack started on the night of the 30th of August and concluded by the 5th of September when Axis units returned to their starting positions.
Lieutenant-General Bernard Montgomery assumed command of the Eighth Army on the 13th of August 1942. He ordered tanks to be used as anti-tank guns in defensive positions on the ridge and decided not to exploit his victory immediately.
The Qattara Depression located 30 miles south of the front line was impassable for tanks, forcing all movement into a narrow corridor between the coast and the depression. This geography allowed the British to concentrate their defenses along the Alam el Halfa Ridge.
Axis supply lines were precarious because Benghazi and Tobruk were 1,000 miles and 650 miles from the front respectively. By the end of August over 50 per cent of supply ships from Italy had been sunk leaving Rommel short of fuel and ammunition.
During the engagement on the 1st of September the Germans lost 22 tanks while the British lost 21. The Axis forces had approximately 200 gun-armed tanks in the two Panzer divisions and 243 in the two Italian armoured divisions.