In Airbnb, open Listings, pick the listing, then go to Calendar → Availability → Connect calendars → Export Calendar and copy the link. Airbnb gives one link per listing, so copy each listing separately.
In Airbnb, open Listings, pick the listing, then go to Calendar → Availability → Connect calendars → Import Calendar. Paste the link and give it a name.
Yes. Export the link from each site, import it into the other, and a booking on one will block those dates on the other.