@NoraDaimio Ummm - yes, in
our world's nobility. Not in the setting of this manwha. You can see they have parties where the children interact with each another directly.
At no point has this author out-right said or even implied this was nobility like the nobility or our world. And the kids are childish - they physically fight and argue - even at other people's tea parties. Heck Lippe's brothers physically rebuke each in public, something an adult noble would probably never do in our world, so they're definitely not acting like 20 year olds. But they have taken etiquette classes so they know the minimal decorum to maintain - which they remember some of the time. If that happens to make them seem more mature, then yup, it's growth of the child, not a mental instability.
And yup, people have already pointed out that Lippe is strange, according to their own common sense. Adults find it cute or endearing since she's acting above her age group, and seems to have beneficial effects on the other children, so they let it go. Elphinny has already pointed out that she is strange. Hal is willing to "play along" with her since she is his friend's little sister, but he also finds her strange. Asterias is special in many ways, so he's an outlier to begin with. Julius and Hilbert both like Lippe so they excuse a lot of her behaviour. And Lippe's family and servants (outside of that one who got fired, and the butler) are too used to her behaviour to think anything of it.
Most of the adversarial adults who have crossed swords with Lippe have found her strange as well. They just don't last long enough in the story to tell us what they did about it. The tutor made the ladies think about why Lippe was so smart (knowing fractions) - but Lippe already thought ahead and had a plausible explanation, which allowed the adults to jump to a conclusion.
At the end of the day, the story requires that Lippe interact with her world simply because it is the only way for her to break the future she came from. If you're not willing to accept the setting of the story, then it's perfectly fine to drop and not read this.