Short answers, pulled from the story.
Batu Khan was a Mongol ruler who lived from roughly 1205 to 1255 and founded the Golden Horde, a part of the Mongol Empire that took shape after Genghis Khan's death. He was a son of Jochi and a grandson of Genghis Khan.
Batu Khan invaded Kievan Rus' beginning in 1237, besieging Ryazan after Yuri II of Vladimir-Suzdal refused his demand for allegiance. His forces sacked the capital of Vladimir-Suzdal on the 4th of February 1238, ransacked fourteen Rus' cities including Rostov, Yaroslavl, and Tver, and stormed Kiev in December 1240.
Batu Khan's invasion of Europe halted because Ogedei Khan died in December 1241, and the Princes of the Blood along with Subutai were recalled to Karakorum for the kurultai. The Mongols withdrew in the late spring of 1242, even though Batu had wanted to continue toward Austria, Italy, and Germany.
Batu Khan never became Great Khan, despite being a potential candidate and being offered the throne at a kurultai he called in 1250. He rejected it and instead nominated Mongke, who was proclaimed Great Khan in 1251.
Batu Khan stood about five feet seven inches tall, roughly 1.70 meters. William of Rubruck described his entire face as covered with reddish spots, and Giovanni da Pian del Carpine called him kind to his own people but greatly feared, most cruel in fight, shrewd, and crafty in warfare.
The Golden Horde ruled longer than any other Mongol khanate, with the descendants of Batu Khan controlling the steppes of present-day Ukraine, Russia, and Kazakhstan. Batu's line ruled the Jochid Ulus until 1360, and after his death in 1255 the horde passed to his son Sartaq and then his brother Berke.