Short answers, pulled from the story.
The earliest known mention is by Shapur I of the Sassanid Empire in the 3rd century CE, who recorded a form of the name as Abgan. Bactrian documents from the 4th century also use the word Afghans, or Afghana, for a distinct clan.
Afghan was originally an ethnonym for the Pashtun people rather than a name for a country. Since the second half of the twentieth century it has broadened into a demonym for all residents of Afghanistan, regardless of ethnicity.
Afghanistan combines Afghan with the Persian suffix -stan, meaning place of. The name appears in the writings of the 16th-century Mughal ruler Babur and came into wider use by 1855, when it was officially recognized by the British during the reign of Dost Mohammad Khan.
Some 19th and 20th century scholars proposed that Afghan derives from Aśvakan, meaning horsemen, related to the Sanskrit and Avestan words aśva and aspa for horse. The theory also links the name to the Assakenoi, ancient Hindu Kush inhabitants named by the historian Arrian, though more recent scholarship has questioned it on linguistic grounds.
Written in 1612 by Nimat Allah al-Harawi, the Maḫzan-e Afġān traces the Afghans to an ancestor named Afghana, described as a grandson of the biblical Saul. It says Afghana's descendants were exiled to the mountains of Ghor after Nebuchadnezzar's attack on the Kingdom of Judah in the 6th century BCE.
The Moroccan traveler Ibn Battuta, visiting Kabul in 1333, wrote that the city had become occupied by Afghans who "possess considerable strength" and were "mostly highwaymen."