I just finished reading those three chapters. What you described seems to be complete. Regarding the conversation about the boy being naughty, I think she is just expecting a male child to act out more than a female child.
Personally, I don't like the style of the writing. The idea of "purple prose" comes to mind. There are way too many adjectives and too many confusing phrases for my taste. I also don't think this is "stream of consciousness" because there is a definite story being told in an orderly fashion. To illustrate my objections, here is the first sentence from the last paragraph of chapter 3:
The great question, or one of these, is, afterwards, I know, with regard to certain matters, the question of how long they have lasted.
There has got to be a simpler way to phrase the "great question". "How long has this been going on?" might be one way to put it.
I do like the dialog between Mrs. Grose and the narrator. I view Mrs. Grose as someone older and different from the narrator and the previous governess who died mysteriously. I see her as someone who knows more than she is saying, but she isn't really sure what is going on.
In any case, the library or internet may have something interesting regarding this story. I haven't checked. I am no expert. Perhaps my comment will get others who know more about this story to offer their insights.