1) Unfortunately, if you are need to make the several reservations per the same timeslot at same date, so its not possible in any versions of Booking Calendar.
At the Booking Calendar Business Small and Business Medium versions are possible to make the bookings for the specific time slot.
Please note, if some visitor will reserve the specific time slot at selected date at specific booking resource (calendar), this timeslot become unavailable for the other visitors at this selected date in this booking resource.
At the Booking Calendar Business Large version is possible to set the capacity of the booking resource, it’s mean that your visitors can make the several reservations per the same date, in other words, the date(s) in calendar will be available until lumber of reservations per these full dates is less than capacity of the booking resource. Please note, if you will use the timeslot selection for the booking resource with capacity higher than one, so then this timeslot will be simply record as a data into DB according this booking, but will not impact to the time availability.
Please read more info about the booking resources and how to configure them here.
2) In the Booking Calendar Business Medium version is possible to configure several custom booking forms. Its mean that inside of the each such booking form you can configure the different timeslots or time fields. After that you can insert into the different pages the specific booking form for the specific booking resource (court).
3) In the Business Medium version is possible to define the condition of showing the specific time fields, depend from the selected date. Please read more about it here.
4) You can define the special links in the email templates, so the visitors, who made the booking, can use them to modify or cancel own bookings. Please read more how to configure it here.
5) As you can see some of the your requirements are not supported, thats why please retest the live demo to be sure in functionality of plugin. Its also possible to make some customization of the plugins source code. Please note, if you will modify the source code of the Booking Calendar, we will not guaranteed the correct work of plugin and do not support it.
P.S. Please post any questions about the paid version of Booking Calendar at the support section of the plugin website here. This support forum is for the free version of Booking Calendar.