Basketball is a sport.. = That would be right, but take off a period if you are ending the sentence. Or if it elipses, then add a period.
Do you do any sport? = If you only want to refer to one sport, put "a" where "any" is. (Also, a better verb would be "play." Do you play a sport?)
Do you do any sports? = This is also correct.
It depends on two things, if it is plural, and what word is used with it.
Hope I didn't confuse you with "the sports" because in that case, it depends on if it is plural or not.
PLURAL EXAMPLE: At my school, most of the sports are in the fall season.
SINGULAR EXAMPLE: For me, the sport I enjoy most is tennis.
Student or Learner