Can my customers schedule an appointment with me on a future date?

Yes, your customers can schedule an appointment for a future date. You can set it up under Event Scheduling in Appointment Pages.

For example, consider this option - How far into the future should customers be able to schedule an appointment?
If you say In the next 5 days, then your customers will be able to see the slots available in the next 5 days and be able to schedule an appointment on one of those days.