The candies Finch catches in his mouth are Mike and Ike, the names he also gives his bodyguards.
At around 20 minutes, Finch says "Let's just say, I have a particular set of skills" quoting Liam Neeson's line in "Taken," a movie about a former covert ops guy trying to rescue his kidnapped daughter.
Music playing while Finch was learning languages was: Babymetal - Gimme Chocolate