Short answers, pulled from the story.
Japan's stated objective was to "deal a major blow to the Ninth Military Front in order to thwart the enemy's plan for resistance." Japanese commanders explicitly emphasized at every opportunity that the goal was not to occupy the area or obtain supplies. The operation was designed as a punishing strike to weaken Chinese resistance, not a conquest.
The Ninth Military Front assembled 378,307 troops in 35 divisions across 13 armies and three army groups throughout Hunan Province. They were headquartered in Changsha under commander Xue Yue, whose plan was to lure the Japanese army south of the Miluo River and destroy it there.
The Japanese 4th Division entered the northeast corner of Changsha at 17:00 on the 27th of September 1941, and the Hayabuchi task force followed at 22:00 the same evening. Japan began withdrawing from the city on October 1, and the withdrawal was fully complete by October 6.
The 74th Corps, commanded by Wang Yaowu, was regarded by the Japanese 11th Army as an elite assault force directly under the Nationalist Government and was the unit they feared most. It fought fierce engagements at Chunhua Mountain and Yong'an city on September 26 and 27, with the 57th Division alone suffering nearly 3,000 casualties in a single day. The 58th Division, the last to withdraw while covering the other divisions' retreat, took the heaviest losses of any division in the entire battle.
The Japanese 11th Army suffered 1,670 killed, 5,184 wounded, and 14 missing in the Changsha battlefield. The Chinese Ninth Military Front suffered 70,672 killed, wounded, or missing across the battle, with the 58th Division alone sustaining 6,192 casualties out of its 11,907 troops.
Liao Lingqi, commander of the 58th Division, was sentenced to death and shot on the 22nd of October 1941 for allegedly deserting in battle. Three of his regimental commanders resigned in protest. Chiang Kai-Shek later rehabilitated him posthumously, ordered an annual pension for his family, and had his body enshrined in the Nanyue Martyrs Shrine.