If she passes all subjects and skips a grade, won't she just end up moving up a grade and not being able to go back home? Also, I'm unsure that just going home makes for a good school life, since networking is probably important between nobles and even talented commoners who may become influential.
She may be worried about passing practical magic, but from what we've seen her everyday magic is absurd.
I don't like it when characters hate the MC for no good reason. I hope she's able to make friends.
There is a good reason though; they are nobility with high status and the pressure to demonstrate that they are worth that high status. They likely had good tutoring to prepare for school so being outdone by anyone is going to be hard to accept, especially since they undoubtedly put some effort into their studies since they were able to get excellent grades on several subjects. Their frustration is understandable.
What wouldn't be acceptable would be if they actually acted against her because of their frustrations and they haven't done that yet.
There probably will be some drama still, otherwise there wouldn't be much story to tell, but I don't think anything really bad. I mean, the prince is there in order to ground his personality so he will be lectured if he actually does anything stupid.
As for the count girl, we don't really know much about her yet, but as I mentioned, networking is important, so if there's a bright student it makes sense that she would want to get acquainted.
We'll just have to wait and see. Seems pretty fun to read for me.