Eat breakfast: Eat breakfast (UK), eat breakfast (USA), usually in English.
Answer the phone: I seldom talk about this when I listen to the phone, and talk on the phone (you don't just listen, do you).
Play the piano: Play/practice the piano.
Chess: chess (chess) (black and white chess, black and white chessboard), if it is chess-China chess.
Mountain climbing: Go hiking and rock climbing.
Outing: Go camping (camping) and have a picnic (picnic).