Short answers, pulled from the story.
Béla IV was King of Hungary and Croatia from 1235 to 1270 and Duke of Styria from 1254 to 1258. He was the oldest son of King Andrew II and is remembered as the "second founder of the state" for rebuilding Hungary after the Mongol invasion of 1241-1242.
The Mongols under Batu Khan annihilated Béla's army at the Battle of Mohi on the Sajó River on the 11th of April 1241. At least half the villages in the plains east of the Danube were depopulated, and a severe famine followed in 1242 and 1243. Béla himself was chased across Dalmatia as far as the fortified coastal town of Trogir before the Mongols withdrew in March 1242.
Béla IV earned that epithet for rebuilding Hungary after the Mongol devastation of 1241-1242. He promoted the construction of close to 100 new stone fortresses, resettled depopulated lands with colonists from neighboring regions, founded the fortified town of Buda in 1248, and granted privileges to more than 20 settlements modeled on Székesfehérvár.
Béla's favoritism toward his younger son Béla, Duke of Slavonia, and his daughter Anna led his heir Stephen to suspect he was being disinherited. Armed conflict erupted in 1264, and Stephen decisively defeated his father's army at the Battle of Isaszeg in March 1265. A peace agreement signed on the 23rd of March 1266 on Rabbits' Island divided Hungary along the Danube, with Béla ruling the west and Stephen governing the east.
Three daughters of Béla IV were officially venerated by the Holy See. Kunigunda was beatified in 1690, Yolanda in 1827, and Margaret was canonized in 1943. A fourth daughter, Constance, became the subject of a local cult in Lemberg, present-day Lviv in Ukraine.
Béla IV died on Rabbits' Island on the 3rd of May 1270. He was initially buried in the church of the Franciscans in Esztergom, but Archbishop Philip of Esztergom had the body transferred to Esztergom Cathedral. The Minorites later recovered his remains after a prolonged lawsuit.