Do countries lose wrong-culture cores when they get annexed? From experience, I would say no, but then this happened:
Milan takes two provinces off the Swiss, hold them for 50+ years, get cores.
Then, they get systematically taken apart by me and some other folks. The Swiss take advantage and take back their two provinces.
Right before I finally get around to annexing Milan, they still have cores on the Swiss provinces. After annexing, however, I notice the cores are gone.
Bear in mind, the AI never uses Promote Cultural Unity.
Second question:
What determines where you get cores when you form the HRE? Same culture group? Accepted culture?
Forming HRE as Italy, I got cores on Burgundian, Bohemian,Swiss, and Austrian land, , but not on the vast majority of the HRE minors. What gives?
Third question:
When inheriting on monarch death (not DW force-inherit), do you only get cores on same culture group provinces that are cored by the junior partner? I noticed something happening along these lines when I inherited an expanded Guyenne as Burgundy. I got cores on the cored Guyenne provinces, but not the new acquisitions on Cosmopolitaine culture provinces.