What a hell of a chapter, thank you very much for translating.
Kate is showing real intelligence in this chapter, and not just getting knowledge straight from the author. For example, she knows that if the star bearers actually told Edward about her, he would be there ready to kill her in a moment. The fact that he isn't there means that they are trying to handle this themselves, understandably as it reflects badly on them. In an instant, she puts together the fact that the current star bearers are over compensating, with the knowledge Oliver gave her that Edward is pressuring them to attack her. And she decides to drive a wedge between them and Edward, a very high risk high reward play. If she just ducked her head out of this she would survive the day, but the star bearers would be desperate to pin any blame on her in the future. This is her only shot of getting the star bearers behind her. I look forward to seeing how she accomplishes this, she will probably point out that if she isn't the culprit and trouble happens again they will all be crucified for not solving the mystery. Edward will throw them all away in an instant, whereas she depends on them for survival. From the perspective of what relationship gives them more power it's obvious. And they all know that Edward has his hands tied as well, he can't simply waltz in and remove Kate or the star bearers, and is even kept from the childrens building for the most part.
If Kate wins this debate and subsequent investigation she will be either a star bearer or as good as one. Once the star bearers cast their lot in with her they have to stay the course no matter what, as Edward will destroy them too if he can. And the shadow of the Great Grandfather looms over it all, its motives vast and unknowable. Why are the children given so much latitude to govern themselves in the first place?
I'm curious about who the real culprit of the incident was. The shadow they met far earlier that caused the last ghost incident is still alive and well, and is probably behind the last incident too. They are almost certainly a rebel, judging by how they broke the coffee by manipulating the twins. The twins will probably die from this, a "broken" doll does not sound pleasant. What happens to shadows that are disposed of? Rosemary is also certainly being controlled, the way that the twins displayed they could already do to Emily. Good foreshadowing on both accounts.
A few other minor notes:
Did anyone else notice how good of a face Emily was being? Apart from the initial shock when Kate took the floor, she's been dispalying perfect expressions.
Barbara is actually showing real leadership of the star bearers, though her doll is still nasty. If she could get her soot under control she could end up being surprisingly good at her job.