I work with a Greek lady, and tried to impress her with my Greek from Assassins Creed: Odyssey by saying "Chaire!" to her. Turns out it's archaic if not actually ancient Greek.
A good source would be epistolography, another would be narration of encounters.
This one seems tricky. English letters do not normally begin with "hello", or even with any synonymous phrase. Instead, they use forms that are specific to written letters.