Short answers, pulled from the story.
The Battle of Luzon began on the 9th of January 1945, when Allied forces landed at Lingayen Gulf, and continued until Japan's unconditional surrender later that year. Allied forces controlled all strategically and economically important locations on Luzon by early March 1945, but Japanese resistance in the mountains persisted for months beyond that.
Between 192,000 and 217,000 Japanese combatants died, the majority from starvation and disease rather than enemy fire. American combatant deaths totaled approximately 8,310 killed and 29,560 wounded. Civilian deaths, overwhelmingly Filipino civilians murdered by Japanese forces, were estimated at between 120,000 and 140,000.
General Tomoyuki Yamashita commanded the Imperial Japanese Army in the Philippines during the Battle of Luzon. He divided his forces into three groups: the Shobu Group in northern Luzon, the Kembu Group in central Luzon, and the Shimbu Group in southern Luzon. After Japan's surrender, it was revealed that Yamashita had been planning to commit suicide if the war had continued.
During February 1945, Japanese forces murdered large numbers of Filipino civilians in and around Manila, accounting for a significant portion of the estimated 150,000 civilian deaths in the overall battle. The battle for Manila itself cost 1,010 American soldiers killed, 3,079 Filipino combatants killed, and around 16,000 Japanese soldiers dead.
The Battle of Luzon included the largest tank battle ever fought between American and Japanese forces. The Japanese 2nd Tank Division fielded 220 tanks while American forces deployed only 76 tanks, supplemented by 105mm M7 Priest self-propelled howitzers and infantry with bazookas. The engagement lasted more than three weeks and resulted in the destruction of around 200 Japanese tanks.
The Philippines, including Luzon, was considered strategically vital because Japan's control of the islands posed a significant threat to U.S. interests in the Pacific. General Douglas MacArthur began arguing for a return campaign shortly after the 1942 Japanese capture, though planning took two years before the campaign launched in 1944. MacArthur targeted the landing at Lingayen Gulf in the north because it gave his forces access to roads and railways leading south through the central plains to Manila.