Live availability is shown in the calendar with instant, automated booking.
Last minute appointments are possible (cut off is set to 30 minutes before the time).
A cut-off-time could be defined too but why not have last minute bookings, if there is vacancy.  The system can handle it, can your staff?

A partial payment (deposit) or full payment could be taken with each booking (refundable with more than 24 hours notice by telephone).
To mitigate ‘no-shows” or to ensure the commitment to the reservation, a full or partial payment can be taken e.g. by PayPal, Bank transfer, or ‘walk-in’.