] ] I understand that when Austen writes &c. that she means etc., as in et cetera but why does she write & instead of et?

] I think"(snip) that it is because in 'et' in Latin means 'and' in English.

yes that's tight. Only would like to add that the symbol for & actually comes from the latin word 'et'. Maybe you can try this out, just write the 'e' bigger than the 't' and if you look at it with some imagination you can see how. I believe there are some fonttypes where it is very clear that the '&' symbol comes from 'et'. (hope make any sense to you)
so when they wrote '&c', they mean 'etc' and as Elizabeth MaryAnne said, it means 'and other things'.