Date available but not as an arrival date - it's something that exists in some booking systems, but not Airbnb currently. Would be a handy feature to cover dates when you're not available to greet new arrivals.
On the other part of the subject, it used to be really obvious how to set exceptions to minimum stay length - it was part of the settings box to the right of the calendar. In the updated layout it's still available, but not so obvious: go to 'Availability', the hit the 'Edit' button by the 'Trip length' header, click the 'Add a requirement for seasons or weekends' link, and then, for custom settings, select 'Specific dates' from the drop-down menu titled 'During'.