Short answers, pulled from the story.
Operation Husky was the Allied invasion of Sicily in July 1943, also known as the Allied invasion of Sicily or the Battle of Sicily. It began on the night of the 9th and the 10th of July 1943 and ended on the 17th of August, lasting six weeks. It was the largest amphibious operation of World War II in terms of the size of the landing zone and the number of divisions put ashore on the first day.
Operation Mincemeat was a British deception conceived by Naval intelligence officer Ewen Montagu and RAF Squadron Leader Charles Cholmondeley. A corpse dressed as a British Royal Marines officer was allowed to drift ashore in Spain carrying fake documents suggesting the Allies planned to invade Greece, not Sicily. German intelligence believed the forgeries and diverted three panzer divisions to Greece and sent Generalfeldmarschall Erwin Rommel there to assume command, reducing the Axis forces defending Sicily.
General Dwight D. Eisenhower served as overall Commander-in-Chief. British General Sir Harold Alexander commanded the 15th Army Group and directed the two invading armies. General Sir Bernard Montgomery commanded the British Eighth Army's Eastern Task Force and Lieutenant General George S. Patton commanded the American Seventh Army's Western Task Force. Admiral Sir Andrew Cunningham served as overall Naval Forces Commander.
Strong winds of up to 45 mph scattered the American paratroopers widely across south-east Sicily and only 12 of 147 British gliders landed on target, with 69 crashing into the sea and drowning more than 200 men. A platoon under Lieutenant Louis Withers seized the Ponte Grande bridge and held it until reduced to 18 men before being forced to surrender just 45 minutes before British ground forces arrived. On the 11th of July, a second airborne drop went wrong when Allied naval vessels mistook incoming C-47 transports for enemy aircraft during an Axis air raid, shooting down 23 of 144 transports and killing 83 men.
The U.S. Seventh Army lost 8,781 men, the British Eighth Army suffered 11,843 casualties, and Canadian forces sustained 2,310 casualties including 562 killed. German losses were estimated at around 20,000-27,940 killed, wounded, or captured depending on the source. Italian military losses according to the Historical Branch of the Italian Army totalled 4,678 killed, 36,072 missing, 32,500 wounded, and 116,681 captured.
The evacuation, codenamed Operation Lehrgang, ran from the 11th to the 17th of August 1943 across the Strait of Messina. The narrow strait was protected by 120 heavy and 112 light anti-aircraft guns and covered by artillery up to 24 centimeters in caliber, making Allied air and naval interdiction largely ineffective. The Germans evacuated some 52,000 troops along with 14,105 vehicles, 47 tanks, and roughly 20,700 tons of stores. Italian forces evacuated approximately 62,182 men.
The fall of Sicily led directly to the ousting of Italian leader Benito Mussolini and the collapse of his regime, which was replaced by the First Badoglio government. Italy's subsequent exit from the war forced Germany to replace Italian forces throughout Italy and parts of the Balkans, diverting one-fifth of the German army from the Eastern Front, a proportion that remained until near the end of the war. The Mediterranean was also reopened to Allied merchant shipping for the first time since 1941.