The title of this episode, "/", is a symbol which means "Root Path" for UNIX-like systems.
The name Root uses for her FBI credentials is "Augusta A. King". Augusta Ada King, Countess of Lovelace was a 19th century mathematician, who worked on an early theory for creating a computing device (the Analytical Engine).
Both Harold and Root are speaking in the opening credits.
Root uses cayenne pepper poured in hot oil to aerosolize the capsaicin (irritant) in the chile, creating instant tear gas. The Chinese used this method to fight off enemies more than two thousand years ago.
Root tells Harold, "The machine offered me a job. She never said it would be easy." This is almost identical to what Harold previously tells John: "When I offered you a job, I never said it would be easy."