Short answers, pulled from the story.
The siege of Kiev lasted from the 28th of November to the 6th of December 1240, a total of nine days. This date range was established by scholar Alexander Maiorov in 2016 after comparing all surviving chronicle accounts, which had previously contradicted each other on the exact timing.
Of roughly 50,000 inhabitants before the invasion, about 2,000 survived. Most of the population was massacred and most of the city was burned, with only six of the forty major buildings left standing.
Voivode Dmytro commanded Kiev's defense while Danylo Romanovych, who held the city for the Principality of Galicia-Volhynia, was in Hungary seeking a military alliance. Dmytro was wounded by an arrow during the fighting but was spared by the Mongols in recognition of his bravery.
During the Mongols' final assault on the 7th of December 1240, a large number of Kievans had taken refuge inside the Church of the Tithes. The building's balcony collapsed under the weight of the people standing on it, crushing many of them.
After the siege, Batu Khan forced Galicia and Volhynia to submit to Mongol suzerainty, and the Mongol army advanced into Hungary and Poland. All major Rus' princes eventually traveled to Sarai, the Golden Horde capital, to formally submit. Michael of Chernigov was executed in September 1246 after refusing to perform the required submission rituals.
The most detailed native account is the Galician-Volhynian Chronicle, completed in the 1290s and preserved in the Hypatian Codex. Foreign accounts include the Jami al-tawarikh by Rashid al-Din Hamadani and the Ystoria Mongalorum by Italian diplomat Giovanni da Pian del Carpine, who visited Kiev in 1246. The sources frequently contradict each other on key details and dates.