Can I include a note on extra-curricular activities in my SOP?
Think about this from the other side of the application: why would these activities cause someone reading the application to believe you a strong candidate for admission to Ph.D study?

If you can make a (non-tortured) case that your teaching skills improved because you taught art, that's a point in your favor; consider including it in the SOP. Badminton doesn't strike me as terribly relevant to molecular biology research, however, so I'd leave it right out.

(The calculus may legitimately be somewhat different for a professional program. The one I teach in looks for community involvement and leadership development, among other things, because both of those augur well for people in the professions we train for.)