Short answers, pulled from the story.
The Mongol army met the forces of several principalities and the remnants of the Cumans under Köten on the 31st of May 1223. This engagement resulted in a decisive Mongol victory over the Rus' coalition.
Batu Khan commanded the force alongside Subutai when it crossed the Volga River to invade Volga Bulgaria. The army consisted of around 120,000 mounted archers who extinguished resistance from the Volga Bulgars, Cumans-Kipchaks, and Alans within one month.
The horde stormed Kiev after many days of siege and ransacked the city immensely though St. Sophia Cathedral survived intact. Giovanni da Pian del Carpine recorded that the city which had around 50,000 people contained scarce two hundred houses with inhabitants kept in complete servitude six years later.
Ivan I of Moscow joined the Mongols in crushing an uprising led by Prince Michael of Tver in 1327. By eliminating his rival he received the title of Grand Prince from the Mongols and allowed the Russian Orthodox Church to move its headquarters to Moscow.
Mongol domination with requisite demands of tribute continued until the Great Stand on the Ugra River in 1480. Although a Russian army defeated the Golden Horde at the Battle of Kulikovo in 1380 full independence was not achieved until the final standoff.