Short answers, pulled from the story.
The First Battle of El Alamein began on the 1st of July 1942 and ended with the cessation of offensive operations on the 31st of July 1942. The battle started when the German 90th Light Infantry Division advanced eastward at 03:00 on the 1st of July.
Lieutenant-General Claude Auchinleck assumed direct command of the British Eighth Army after relieving Lieutenant-General Neil Ritchie on the 25th of June 1942. Bernard Montgomery later took command of the Eighth Army on the 13th of August following the death of William Gott.
The British chose to defend a line stretching between the Mediterranean Sea and the Qattara Depression south of El Alamein. This position prevented Axis forces from outflanking them without crossing the Sahara Desert.
The Eighth Army suffered over 13,000 casualties in July including 4,000 men from the 2nd New Zealand Division and 3,000 from the 5th Indian Infantry Division. The battle resulted in heavy damage to Axis men and machines while capturing 7,000 prisoners.
Rommel failed to break through because his exhausted forces could make no further headway without resting and regrouping after repeated counter-attacks. His three German divisions numbered just 1,200 to 1,500 men each due to resupply problems caused by Allied air interference.