Robert notes that Mary "...has more suitors than the Princess Aurora," referencing the protagonist of "The Sleeping Beauty," an 1889 ballet by Pyotr Ilyich Tchaikovsky.
In the church with Edith, Matthew asks if a missing screen was "a Cromwell casualty." Oliver Cromwell was a military leader with the Parliamentarians, who battled the Royalists during the English Civil War (1642-1651). Cromwell wanted churches to reflect his own Puritan values and it may have been that the screen was removed because it was immodest.
Lady Mary says 'Just making sure everything is ship shape and Bristol fashion.' This is a phrase meaning in good and seaman-like order, as on a ship. The expression had its origin when Bristol was the major west coast port of Britain. It's used very little now, if at all.
The "Albanian talks" Mr. Pamuk is taking part in refers to the London Conference of 1912-1913, an international summit in which the future of Albania was to be determined. Albania had declared its independence during the First Balkan War.