Short answers, pulled from the story.
The Battle of Kulikovo was fought on the 8th of September 1380 at Kulikovo Field near the Don River, in what is now Tula Oblast, Russia. The Russian army crossed the Don on the morning of the battle, destroying the bridges behind them to cut off any retreat.
Grand Prince Dmitry of Moscow commanded the Russian forces. After the victory, he received the honorific Donskoy, meaning "of the Don." Dmitry famously exchanged clothes and horses with his boyar Mikhail Brenok so he could fight in the frontlines unrecognized.
Mamai was a powerful military commander and de facto ruler of the western Golden Horde, serving as son-in-law and beylerbey of the slain Khan Berdi Beg. He was not a Genghisid and therefore could not rule as khan himself, forcing him to rule through puppet khans. He attacked Moscow in 1380 partly to reassert tribute demands and partly because his rival Tokhtamysh was closing in from the east, making a show of force essential to his survival.
There is no reliable count. Chronicle estimates of 150,000-400,000 Russian troops are considered completely unreliable by historians. By 2014, archaeologist Dvurechensky estimated the Russian army at 6,000-7,000 warriors, a figure supported by analysis of medieval demography and mobilization capacity. The Tatar army's size is unknown; no sources from the Tatar side survived.
No. Despite the Russian victory, Mongol domination continued. In 1382, just two years after Kulikovo, Khan Tokhtamysh burned Moscow and forced Dmitry Donskoy to accept him as sovereign. Russian vassalage to the Golden Horde officially ended only in 1480, a century after the battle, following the Great Stand on the Ugra River.
The battle generated an unusually large body of medieval Rus' literature, known collectively as the Kulikovo cycle. Its major works are the Chronicle Tale, the Zadonshchina ("The Battle beyond the Don"), and the Skazanie o Mamaevom poboishche ("The Tale of the Battle with Mamai"). As of 2022, over a hundred manuscript copies of the "Tale" have survived, compared to only six known manuscripts of the Zadonshchina.