Short answers, pulled from the story.
Shakespeare changed the character name from Oldcastle to Falstaff by 1598 when the quarto edition listed the character as Sir John Falstaff instead. The play likely appeared around 1596 with the name Oldcastle still attached before William Brooke, the 10th Baron Cobham, complained about the portrayal.
A historical knight named John Oldcastle died as a martyr for his religious beliefs in 1417 and served as the basis for the comic character's original name. William Brooke, the 10th Baron Cobham, was a descendant of the executed heretic and held significant power at court which forced Shakespeare to change the name before publication.
Sir John Fastolf fought against Joan of Arc at the Battle of Patay but escaped capture while others perished despite losing his knighthood temporarily. He became a scapegoat for the English defeat and the new name probably derived from this medieval figure who avoided death or injury.
Mistress Ford and Mistress Page tricked him into hiding in a laundry basket full of filthy clothes awaiting laundering and later made him disguise himself as the fat woman of Brentford. They eventually had local children dressed as fairies attack him by an old oak tree in Windsor Forest pinching and burning him to punish him.
Giuseppe Verdi wrote his last opera Falstaff in 1893 with a libretto by Arrigo Boito mostly based upon The Merry Wives of Windsor. Other composers like Otto Nicolai created Die lustigen Weiber von Windsor in 1849 which remains one of the most famous versions.