Short answers, pulled from the story.
William Pitt the Younger became prime minister at the age of 24 in December 1783, making him the youngest prime minister in both British and world history. He had been born on the 28th of May 1759.
William Pitt the Younger served as prime minister for eighteen years and 343 days across two separate terms, making him the second-longest-serving British prime minister after Robert Walpole. His first term ran from 1783 to 1801, and his second from 1804 until his death in 1806.
Pitt resigned on the 16th of February 1801 ostensibly over Catholic emancipation, which King George III refused to grant. Later research by his biographer suggests the actual reason was his desire to make peace with France, which he could not achieve against opposition from the King and Cabinet; he engineered the resignation to remove opponents of peace and allow Henry Addington to take office.
Pitt introduced Britain's first income tax, suspended the convertibility of banknotes to gold in 1797 to protect the kingdom's reserves, established a sinking fund of £1 million per year in 1786 to reduce the national debt, and cut tariffs on smuggled goods like tea and tobacco, raising customs revenues by nearly £2 million a year. By 1792 the national debt had fallen from £243 million to £170 million.
Beginning in September 1793, Pitt ordered an invasion of the French Caribbean colony of Saint-Domingue to use it as a bargaining chip against France. The campaign became a catastrophe: yellow fever and armed resistance killed roughly 50,000 British soldiers and sailors, with another 50,000 rendered unfit for service. The last British troops withdrew on the 31st of August 1798 after Colonel Thomas Maitland negotiated a withdrawal with Governor-General Toussaint Louverture.
Pitt and Wilberforce first became friends at Pembroke College, Cambridge, and remained lifelong allies in Parliament. Wilberforce led the campaign to abolish the slave trade, which Pitt supported but never managed to complete. The Slave Trade Act passed in 1807, the year after Pitt's death. Wilberforce said of Pitt, "For personal purity, disinterestedness and love of this country, I have never known his equal."