Hello.
1) If you need to make the specific number of bookings per days, then you need to check the Booking Calendar Business Large version, where is possible to make several reservations per specific FULL date(s) by visitors (not time slots). Please read more about it here http://wpbookingcalendar.com/overview/#capacity
At this version is 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 is 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 http://wpbookingcalendar.com/help/booking-resource/
Also we highly recommend to check this article about different configuration of capacity and availability http://wpbookingcalendar.com/faq/capacity-concept/
2) The Business Small and higher versions of the Booking Calendar is support PayPal (Standard and PayPal Pro Hosted Solution (please note, PayPal PayPal Pro Hosted Solution its does not the same as PayPal Pro)), Authorize.Net, Sage Pay, iDEAL via Sisow and iPay88 payment gateways integration, other payment systems are not supporting yet. You can configure and activate it at the Booking > Settings > Payment page.
If you want to make the integration of your payment system by yourself, so you will be able to check how was integrated exist payment system in plugin like PayPal or Sage Pay gateways. Please check more about this here: http://wpbookingcalendar.com/faq/custom-gateway-in-7-0/
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.
You can test Booking Calendar live demos at this page http://wpbookingcalendar.com/demo/ to be sure in functionality and do not have misunderstanding.
Kind Regards.