Short answers, pulled from the story.
The Second Battle of El Alamein was fought from the 23rd of October to the 4th of November 1942, near the Egyptian railway halt of El Alamein. The battle lasted 13 days and ended with the Axis Panzerarmee Afrika forced to retreat from Egypt and Libya to the borders of Tunisia.
Lieutenant-General Bernard Montgomery commanded the British Eighth Army at El Alamein. He had been flown from Britain to replace Lieutenant-General William Gott, who was killed when his transport aircraft was shot down by Luftwaffe fighters before the battle began.
The Eighth Army fielded 195,000 men and 1,029 tanks against the Panzerarmee Afrika's 116,000 men and 547 tanks. By the end of the battle on the 28th of October, the Eighth Army still had 800 serviceable tanks while the Panzerarmee reported only 81 serviceable German tanks and 197 Italian.
British Ultra intercepts and local sources exposed the Axis order of battle, supply position, and intentions, giving the Eighth Army a decisive advantage. Intelligence identified Axis supply ships and their cargoes, allowing them to be attacked, and by the 25th of October Panzerarmee Afrika was down to just three days' supply of fuel. Until June 1942, Rommel had benefited from stolen American diplomatic codes, but that advantage ended after the 9th Australian Division captured the German 621st Signal Battalion in July 1942.
Operation Supercharge was the decisive Allied assault launched at 01:00 on the 2nd of November 1942, spearheaded by the 2nd New Zealand Division and the 9th Armoured Brigade. The 9th Armoured Brigade attacked the Axis gun line on the Rahman track with 94 operational tanks; 70 were destroyed and 230 of the 400 men involved were killed, wounded, or captured, but the assault broke open the Axis defences and triggered Rommel's decision to retreat.
On the 27th of October 1942, the 2nd Battalion the Rifle Brigade held an isolated position called Snipe against repeated German and Italian armoured attacks, destroying 22 German tanks and 10 Italian tanks with thirteen six-pounder anti-tank guns and six more from the 239th Anti-Tank Battery. The regiment's historian described it as the most famous day of the regiment's war. Lieutenant-Colonel Victor Buller Turner was awarded the Victoria Cross for his leadership of the battalion.