Yes, unfortunately you will be penalized if you cancel. The guest can cancel rather than put in a request. However, they do not have to (it would be more as a favor to you), so you might have to do it. So you are aware, the penalties include blocking those dates for further bookings (not a problem in this case), ineligibility for superhost status for a year, and potentially a monetary penalty.
If is the responsibility of the host to keep the calendar up to date. I agree that it is tricky in the beginning to figure out all the details. my recommendation for the future is to check your listing, and particularly the calendar regularly.