Short answers, pulled from the story.
The Mongol Empire was the largest contiguous empire in history. At its height it stretched from the Sea of Japan to Eastern Europe, reaching north into Siberia and south into the Indian subcontinent, and west as far as the Levant and the Carpathian Mountains.
The Mongol Empire was founded by Temüjin, who took the title Genghis Khan. A council proclaimed him ruler of all Mongols in 1206 at a kurultai, where the shaman Teb Tenggeri named him khan of the Great Mongol Nation.
Genghis Khan died on the 18th of August 1227. He named his third son, Ögedei, as his heir, and by his death the empire ruled from the Pacific Ocean to the Caspian Sea, twice the size of the Roman Empire at its height.
The Mongol Empire split because of wars over succession and a dispute over whether to adopt a sedentary, cosmopolitan life or remain nomadic. By Kublai Khan's death in 1294 it had fractured into the Golden Horde, the Chagatai Khanate, the Ilkhanate, and the Yuan dynasty in China.
The Mongol Empire used a relay system called the Yam, built from guarded posts known as örtöö. A messenger typically traveled 25 miles between stations, taking a fresh horse or passing the mail along, and riders regularly covered 125 miles a day, faster than the Pony Express 600 years later.
The Mongol military relied on horse-archers, mobility, and strict discipline organised through a decimal system that dissolved old tribal loyalties. Their total strength in Genghis's lifetime was likely only 50,000 to 75,000 soldiers, so their cohesion mattered more than numbers, since they were almost always outnumbered.
The Mongol Empire's parts fell over centuries. The Ilkhanate disintegrated between 1335 and 1353, the Yuan dynasty lost China in 1368 when Ming forces took its capital, and the Golden Horde's rule in Eastern Europe is traditionally considered to have ended in 1480 at the Great Stand on the Ugra River.