Hello.
1) Booking Calendar plugin is supporting
– import of events via .ics feeds from Google Calendar ( or Airbnb or any other calendar that support .ics format, like iCal application)
– and export bookings to .ics feeds (files), which possible to import in Google Calendar (or Airbnb, Booking.com, HomeAway, TripAdvisor, VRBO, FlipKey and any other calendar that uses .ics format ).
Please read more about this feature here: https://wpbookingcalendar.com/faq/#sync
Import.
Please check about the configuration of import events from .ics feeds in this FAQ instruction here https://wpbookingcalendar.com/faq/import-ics-feeds/
Please note, the import process is working in that case, when some visitor is open your website page with booking import shortcode. So you can configure CRON at your server, for periodically access this page with booking import shortcode to start import process. Or you can insert the import shortcode before booking form shortcode, so firstly system will start import process and only then show booking form, when someone visit your page.
In case if you are having some issue of not ability to import new events, then check this troubleshooting instruction: https://wpbookingcalendar.com/faq/ics-importing-issue/
You can define CRON at your server for periodically access pages with import .ics feeds shortcodes and start import process during specific time-intervals, then check this: https://wpbookingcalendar.com/faq/cron-script/
Export.
Please check about the configuration of export .ics feeds in this FAQ instruction here https://wpbookingcalendar.com/faq/export-ics-feeds/
Booking Calendar is generate .ics feed with bookings in real time. But how often some service (like airbnb, or booking.com ) access this .ics feed to import the bookings from Booking Calendar into own system, does not depend from Booking Calendar. So in other words, Booking Calendar does not force to generate import process by third party service, when some booking is created. You need to check with support of this service (like airbnb or booking.com), about how often they can access the .ics feed tor making import.
2) Unfortunately, the Booking Calendar does not support integration with WooCommerce plugin. Sorry.
Kind Regards.
