My wife and I are so excited to make our first visit to CTI in 12 days. (5/26~6/2)

If anyone has played tennis there before, could you tell us whether they strictly require to wear the proper tennis shoes?
Our goal is to avoid bringing too many things and to use our casual shoes when playing tennis. Any thought that this might be a problem?
Also, I suppose they would rent all equipment there.
Lastly, how busy is tennis court in general?

Thank you for your feedback in advance!