[ETA: Roman numerals are unnecessary, but usually they're not too much trouble. Not sure why I misread the chapter heading, but you'll note that this post now has the correct chapter in the title. We're up to 6, not 7 - or VI, not VII, as the Project Gutenberg edition has it.]
One of the first things that jumped out at me in this chapter is "the girls here were all called by their surnames, as boys are elsewhere." Because that was the case not only for schoolboys, but also for higher-level servants - Darcy's housekeeper is referred to as Reynolds, for instance, in Pride & Prejudice. Is this a dig at the girls' in-between social status - well-bred enough to be sent to school, but not likely to end up as gentry?
This chapter also marks the first time Helen Burns is introduced by name, and it's clear that she's being set up as a foil to Jane - Jane can't even stand to watch Helen be punished, while Helen just accepts it, because clearly, she must have done something wrong.
(That punishment, incidentally? I'd love to think that it's because of Miss Scatcherd's love of black humor that she delivers a switching on the back of Helen's neck in the midst of a lesson on Charles I, but we're never led to think she's that clever.)
So on the one hand, we have Jane: "If she struck me with that rod, I should get it from her hand; I should break it under her nose."
And on the other, Helen: "Yet it would be your duty to bear it, if you could not avoid it: it is weak and silly to say you cannot bear what it is your fate to be required to bear."
Helen seems just a bit too good to be true, which is one of the reasons why it's generally accepted that Charlotte Bronte based the character on her sister Maria, who (spoiler alert) died at the Lowood-esque school the girls attended. So while the idealization is understandable, I think it's fair to say that Jane Eyre would not have been such a success if we had to put up with Helen for more than a couple chapters.