"must be doing her harm..."
See in text (Volume I - Chapter III)
This is a great illustration of the rigid English class structure of the 19th century: Emma is worried that the Martins, who are not of Emma's or, by extension, Miss Smith's class, are not good enough for Miss Smith and may be bringing her down from her natural social standing even though they are "good people." Being good in this society was just not good enough.
See in text (Volume I - Chapter IV)
The Elegant Extracts of Prose and the Elegant Extracts of Verse were books compiled by Vicesimus Knox, an educator who encouraged education for both males and females—an enlightened view in Austen's day.
See in text (Volume I - Chapter XVI)
The British at this time are quite aware of social rank, as well as society's rules of acceptability about connecting with someone of a different rank.