Short answers, pulled from the story.
The Battle of Hengyang lasted 47 days, from the 23rd of June to the 8th of August 1944. The Chinese 10th Army defended the city against repeated Japanese offensives until the headquarters fell in the early morning of the 8th of August.
The Chinese 10th Army entered the battle with 16,275 officers and soldiers, according to Hengyang historian Pei Xiao. By the end of July 1944, only around 3,000 combat troops remained, spread across four heavily depleted divisions.
Ichigo was a Japanese military plan approved by the emperor in January 1944 with two phases: seizing control of the Beijing-Wuhan Railway and then taking the Wuhan-Guangzhou and Hunan-Guangxi Railways. Hengyang sat at the junction of those two major railway lines and was the gateway to Guangxi, Guizhou, Yunnan, and Sichuan, making it essential to Japanese overland control of central China.
Lieutenant General Fang Xianjue commanded the Chinese 10th Army during the battle. He designed the elaborate defensive works, led the 47-day resistance, and on the 8th of August 1944 was captured by Japanese forces. He refused to lead a Japanese puppet army and escaped captivity on the night of the 18th of November 1944.
The 14th Air Force, based at the Hengyang Airfield before the battle, flew continuous missions attacking Japanese supply lines along the Yangtze and Xiang rivers and supporting Chinese defensive positions. At its peak the airfield held 400 planes and more than 2,000 pilots and ground personnel. Chinese defenders credited the air force's daytime dominance with forcing Japanese ground troops to attack at night, making their offensives significantly more difficult.
Chinese relief forces were deployed piecemeal rather than in concentrated strength, and Japan broke Chinese radio codes on the 23rd of July 1944, allowing them to intercept orders and position blocking forces ahead of relief columns. When Hengyang fell on the 8th of August, most reinforcements were still around ten miles from the city. A Chinese National Defense review later acknowledged that forces were applied one by one rather than bringing maximum power to bear.