If I purchase my ticket from the Greyhound app when I get to the Greyhound bus station do I just show them the confirmation email of the ticket or do I have to purchase a new one

If you purchase a "Will call" ticket you can pick it up at the station with the confirmation number. If you purchase a print at home ticket you must print your own ticket.

Yes it is correct need ticket paper

Is the bus terminal inside the airport or do I have to leave? Is there signage? Thank you

If youve already purchased your ticket on the app & have the confirmation num. Give them that nimber at the station, then they will look it up in the system, & then print out your ticket