Hello.
1) Its possible to make the new bookings on the front-end (on the page(s) where you inserted the booking form) or on the back-end side at the Booking > Add booking page.
2) You can manage (approve / cancel) any bookings from the admin panel at the Booking Listing or Calendar Overview pages.
3) In the Booking Calendar Business Large version, where possible to make several reservations per specific FULL date(s) by visitors (not time slots). At this version possible to set capacity of the booking resource, so date(s) in calendar will be available until number of reservations is less then capacity of the booking resource. But in this version possible to make reservation only for FULL date, not a time slots (time slots in this version only record data in the DB, but do not play any logic in reservation). Please read more info about the booking resources and how to configure them here.
4) The “shopping cart” functionality (selections f the several days from the different booking resources) does not support. Sorry.
5) The Business Small and higher versions of the Booking Calendar support PayPal (Standard and PayPal Pro Hosted Solution), Authorize.Net, Sage Pay and iPay88 payment gateways integrations. You can configure and activate it at the Booking > Settings > Payment page.
6) You can test Booking Calendar live demos at this page.
Please contact about the functionality or configurations of the paid versions of Booking Calendar on the support forum of the Booking Calendar or directly here.
Kind Regards.