Short answers, pulled from the story.
A grammarian taught ancient poets like Homer and Virgil alongside language mechanics to prepare boys for higher studies under a rhetorician. This second stage of traditional education focused on correct speech before advancing to rhetoric.
Dionysius Thrax defined grammar as an acquired expertise of general usage among poets and prose writers around 100 BC. He identified six elements including accurate reading aloud and explanation of literary devices.
Marcus Antonius Gnipho was originally brought to Rome as a captive into the household of Julius Caesar. Twelve of the twenty grammarians described by Suetonius had been slaves who rose to become influential teachers within the empire.
Latin grammarians came from all over the Roman Empire including Syria Spain Gaul Athens and Italy. Greek equivalents shared this diverse geographic origin across the vast territory while teachers traveled from distant provinces to instruct students in major urban centers.
Some grammarians achieved elevated positions in Rome despite their relatively lowly jobs and often humble origins. They were exempt from local taxes according to Suetonius Iul. 42.1 even though few enjoyed financial success during their careers.