The Turks enslaved a lot of people—pirate raids, capturing people traveling by sea, and through the “blood tribute” (taking Christian boys from rural areas of the empire and forcing them to become Muslims). If some of those enslaved had offspring there could be Turks with Greek, Bulgarian, Serbian, Italian or other ancestries.
Exactly right. War tended to mix up bloodlines. They especially liked blond, blue eyed slaves from Ukraine, Russia, and other slavic countries. If the Turks had not been stopped at the Seige of Vienna, there might have been a lot of genes from western Europe too.