Because you are need to make the bookings Friday to Friday, you are need to check the Business Small or Business Medium versions, where is possible to use the fixed time as check in/out times for possibility to use the last check out date as check in date for the other bookings.
1) You can create the 2 booking resources at the Booking > Resources page for the each of your properties and then insert the booking forms for the each of your properties. If you are want that your visitor will make the booking for the 2 properties during one reservation process, probabaly you are need to check this info : http://wpbookingcalendar.com/faq/booking-many-different-items-via-one-booking-form/
But usually you will have the different forms with calendars for the each of your properties.
2) Its not possible to set such different duration of stay, which is depend from the check in date. You can define only one week day as check in or set the any week day as check in. for this, please open the General Booking Settings page and activate the "range days selection" using 2 mouse clicks and then configure the minimum or fixed number of days selections.
Also at the same page, please activate the fixed time, and set start time as 13:00 and end time as 12:00. Its for possibility to use the check out date as check in for the other booking.
3) The Business Small and higher versions of the Booking Calendar is support Paypal (standard/pro hosted solution), Sage pay and ipay88 payment systems integrations, other payment systems or direct credit cards payments are not supported yet.
You can test Booking Calendar live demos at this page to be sure in functionality and do not have misunderstanding.
Please read the Booking Calendar version overview here:
Please ask more questions at the support section of the plugin site here: or directly by email.