When it comes to choosing the commoner who enters the school, they aren't chosen through a test of character and intelligence or something, but through a lottery. Good God, whoever founded that school was an idiot.
The fact that Dame Devin not only murdered Blair's biological parents, but also attempted to murder Blair herself when she was just a baby.
Since Dame Devin was apparently a commoner who married into royalty and was said to be Queen Isabella's sister-in-law, it can be assumed that whoever Dame Devin's husband (Delancy's father) was, he was the younger brother of either King Reginald or Queen Isabella (probably the latter, since Kings are born into royalty). This would technically make both Dame Devin and her daughter princesses.
Another possible explanation is that Dame Devin was a Gold Digger who seduced Isabella's younger brother on purpose. That is most likely, as Delancy is next in line for the throne, which that means her father must have been royalty and also in line for Gardenia's throne. As Delancy's father is never alluded to, it can be supposed Dame Devin killed him too, as he lost his utility after Dame Devin conceived an heiress.
Its also possible Isabella was royal by birth and her husband wasnt, meaning Dame Devin wasnt, and the reason Delancy is a princess is because shes the only living blood relative of the last royal family. Keep in mind movies arent bound by how real world royalty works. Because Dame Devin was a lottery winner, I would assume she wasnt tied to royalty at all until her brother married Isabella. Her family probably wasnt even super wealthy. Its likely Isabella and Dame Devin went to PCS together and thats how Isabella met Dame Devins brother- at graduation/Coronation. Dame Devin doesnt even have a royal title- shes got the equivalent of a knighthood title. Dame is a step down from most of not all royal titles. So that also rules out the possibility she has royal blood. She and her brother were probably commoners until her brother married Princess Isabella and became king soon after.
Why don't the princesses receive lessons in economics, international law, or diplomacy? Are they all expected to become figureheads instead of actual monarchs?
Maybe said lessons were when they are seen reading or using a computer. And for the princesses who are not heiresses (re: have older siblings), they will most certainly become figureheads. Blair is not seen attending such lessons in her Training Montage song, but this is most likely because she was there as a Lady Royal student instead of princess. Given that she's revealed to be an actual monarch in the end, she will most likely need summer lessons in economics and international law.