"She's a youngster who needs help and whom I'm deeply interested in helping." (2)
The asker of this question is never specified; it could be a teacher or a counselor, but certainly someone in a position to "help." The question suggests that the asker, whoever it is, doesn't know Emily well enough and needs her mother's insight.
I did like all the books then said. (6)
The narrator mistakenly puts her trust in authority – in this case, medical authority. But see Emily's attitude toward authority in quote #9.
They persuaded me at the clinic to send her away to a convalescent home in the country [...] (26)
The voice of power in the story is often referred to as a "they." Here medical authorities at the clinic convince the narrator to send Emily away to a convalescent home, as if just keeping her way from her working-class mother will make her better. (It doesn't.)