I look forward to seeing him humbled, though I wonder if it will involve humiliating his parents or they will turn out to be reasonable and punish him themselves.
My guess is they'll show up and initially act haughty when they don't know the situation, but during the meeting they'll realize she's reasonable and their son will pull some freak-out that'll make them snap at him and realize she was in the right.
That was fmc rebutting what was said earlier because from what she had seen he seemed to judge her not on her being a commoner but on her abilities.
Yeah, pretty much this.
I assume that the truth is that he's just extremely meritocratic, and in this world there's a pretty direct tie between nobility and magic ability due to education (and also manners, which nobles are taught more). So everyone else thinks that he cares about nobility for nobility's sake, but he probably sees through Aoi's actual magic ability + her demeanor, and realizes that even though she's a commoner, she meets the criteria for what he approves of in people, so he approves of her and she doesn't feel the judginess she was expecting.