Short answers, pulled from the story.
The Battle of Leyte began on the 17th of October 1944 with preliminary operations and the main amphibious landings occurred on the 20th of October 1944. Organized resistance on Leyte was declared over on the 25th of December 1944, and operational control passed to the Eighth Army on the 26th of December 1944.
The U.S. invasion of Leyte, codenamed Operation King Two, aimed to begin the liberation of the Philippine Archipelago from nearly three years of Japanese occupation. Capturing the Philippines would isolate Japanese military holdings across China and the Pacific, and air bases on Leyte could strike enemy positions anywhere in the Philippines. The decision to invade was made at a July 1944 meeting in Hawaii between President Roosevelt, General MacArthur, and Admiral Nimitz.
The Battle of Leyte saw the first major warship sunk by a kamikaze attack. On the 25th of October 1944, a kamikaze pilot crashed into and sank the escort carrier USS St. Lo in Leyte Gulf. The Japanese turned to kamikaze tactics after conventional air raids were no longer effective, with American counterattacks reducing Japanese air strength by the 28th of October.
The Battle of Leyte Gulf, fought from the 23rd to the 26th of October 1944, was the largest naval battle in the Pacific and one of the largest in history. It was triggered by the Imperial Japanese Navy's attempt to destroy American naval forces supporting the Sixth Army on Leyte. Despite a decisive Japanese defeat, Japan still managed to move more than 34,000 troops and over 10,000 short tons of material to Leyte by the 11th of December.
Japanese losses were severe: the army lost four divisions and several combat units, while the navy lost 26 major warships, 46 large transports, and hundreds of merchant ships. Japanese land-based air capability in the Philippines was reduced by more than 50%. American casualties included 49 killed and 192 wounded on the first day of landings alone, with the final drive on Ormoc costing 123 killed, 329 wounded, and 13 missing.
After wading ashore at Red Beach on the 20th of October 1944, MacArthur broadcast to the Philippine people: "People of the Philippines, I have returned! By the grace of Almighty God, our forces stand again on Philippine soil." The statement fulfilled his 1942 vow to return after being ordered by President Roosevelt to leave the Philippines to prevent his capture by the Japanese.