Short answers, pulled from the story.
Edward III became King of England on the 25th of January 1327, when he was proclaimed king in London after his father Edward II was forced to relinquish the throne. He was crowned at Westminster Abbey on the 1st of February 1327, at the age of fourteen.
The Hundred Years' War was a series of conflicts between England and France that ran from 1337 to 1453. Edward III triggered it by claiming the French throne as the grandson of Philip IV of France, after Philip VI of France confiscated Edward's Duchy of Aquitaine in 1337. The French rejected his claim based on precedents for agnatic succession set in 1316 and 1322.
The Order of the Garter is a chivalric order founded by Edward III, probably in 1348. According to Polydore Vergil, the order took its name and motto from an incident at a ball in Calais, where Joan of Kent dropped her garter and Edward silenced the crowd's mockery by tying it around his own knee with the words honi soit qui mal y pense, meaning "shame on him who thinks ill of it".
The Black Death struck England with full force in 1348, killing a third or more of the population. The resulting labour shortage drove wages upward, prompting Edward and Parliament to pass the Ordinance of Labourers in 1349 and the Statute of Labourers in 1351, which fixed wages at pre-plague levels. These measures ultimately failed and the resentment they generated contributed to the Peasants' Revolt of 1381.
Alice Perrers was originally a lady of Queen Philippa's household, appointed by 1359. After the Queen's death she is believed to have become Edward's lover. The Good Parliament of 1376 accused her of taking 2,000 to 3,000 pounds in gold and silver per year from the royal treasury. She received gifts from Edward that included 50 manors across 25 counties and 20,000 pounds in jewels, and was banished from court by Parliament though she returned before Edward's death.
Edward signed letters patent in 1376 placing his third son John of Gaunt second in the line of succession, bypassing Philippa, daughter of his second son Lionel of Antwerp. This decision sent the throne to the House of Lancaster in 1399, while Lionel's descendants formed the basis of the Yorkist claim. The resulting rivalry between the two lines of Edward's descendants helped fuel the Wars of the Roses in the fifteenth century.