Hello.
1) The ability to book for the specific times only possible in the Booking Calendar Business Small / Business Medium versions (and in higher versions for booking resources with capacity =1). Please note if you will make the booking for the specific timeslot, this timeslot become unavailable for the other visitors for that selected date in current specific calendar.
Please watch more in this video: https://wpbookingcalendar.com/help/booking-calendar-video-timeslots/
You can configure the timeslots selections on the Booking > Settings > Form page. Please use the “shortcode generator” on the right side of that page for the correct generation of the shortcode.
You can use one”timerange” (timeslots) or “start time” and”end time” selections or”starttime” and “duration”of time selections shortcodes or even start time and end time entering shortcodes. Please read more about the booking form fields configuration here https://wpbookingcalendar.com/faq/booking-form-fields/
You can test the bookings for the specific time-slots in action on the live demo of Business Small version (which is configured by default for the bookings of specific time-slots) here: https://bs.wpbookingcalendar.com/ Other live demo you will need to reconfigure.
2) The Business Small and higher versions of the Booking Calendar is support Stripe, 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.
Please watch more in this video: https://wpbookingcalendar.com/help/booking-calendar-video-payments/
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 Stripe payment gateway. Please check more about this here: https://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.
Kind Regards.