Short answers, pulled from the story.
Archibald Percival Wavell, born on the 5th of May 1883, was a Field Marshal in the British Army who served in the Second Boer War, the Bazar Valley Campaign, the First World War, and the Second World War. He lost his left eye at the Second Battle of Ypres in 1915 and rose to become Commander-in-Chief Middle East, Commander-in-Chief India, and Viceroy of India before retiring in February 1947.
Operation Compass was Wavell's offensive launched in December 1940 against the Italian Army in the Western Desert of Egypt and Libya. It began on the 9th of December 1940 with the Battle of Sidi Barrani and led by February 1941 to the capture of 130,000 Italian prisoners at the Battle of Beda Fomm and the destruction of the Italian Tenth Army. It remains one of the most decisive British military successes of the Second World War.
Churchill replaced Wavell with Claude Auchinleck on the 20th of June 1941 after the failure of Operation Battleaxe, which attempted to relieve the Siege of Tobruk. Churchill believed Wavell had not exploited available intelligence effectively, though publicly he could not reveal that the intelligence came from broken German codes. Historian David Reynolds concluded that Churchill did not fully understand the difference between the British advantage in strategic code-breaking and the German advantage in tactical field intelligence.
Wavell was Commander-in-Chief Middle East during the Battle of Crete, which began on the 20th of May 1941 when German airborne forces attacked. His forces had prior knowledge of the German plan through broken Luftwaffe codes, but the on-the-ground commander Bernard Freyberg kept most troops on the coast expecting a seaborne assault. By the 1st of June 1941, Wavell had evacuated the last 16,000 Allied troops; approximately 16,000 Allied soldiers had been killed or captured in the campaign.
Their relationship was persistently strained. Churchill called Wavell a "good, average colonel" after their first meeting on the 12th of August 1940 and considered sacking him that summer. Churchill regarded Wavell's quiet manner as a lack of aggression and viewed his poetry writing as unsuitable for a British general. The tension sharpened over Operation Battleaxe and culminated in Wavell's relief from Middle East Command in June 1941.
Wavell swapped positions with Auchinleck and became Commander-in-Chief, India, a post he held from July 1941 until June 1943. Within a month of arriving, he launched an invasion of Persia in cooperation with the Russians to secure oil fields and communications lines to the Soviet Union. He then served as Viceroy of India until his retirement in February 1947, and died on the 24th of May 1950.