BS”D
Playing: Machlokes between the Charaidim in EY (such as Rav Shteinman) and America (such as Rav Reuven Feinstein). There was actually a big commotion regarding this at one of the Agudah conventions from what I hear.
Watching prof sports: On TV? see TV. In person? see Going to a game.
going to a game: My Rov and Rebbe disagree on this one. IIRC there was also a Chinuch roundtable regarding this question. Personally I think it depends on one’s motives (from what I have discussed with both my Rov & Rebbe).