Do other people who live outside Death City know about the DWMA and about Demon Weapons? Or is it some covert operation in an attempt to secretly purge the world of evil? I am unsure if this is a known fact that has evidence to support it or simply up to one's own interpretation.
Yes. The DWMA is actually a famous school. In soul eater not, when Tsugumi finds out that she is weapon and decides to go to the DWMA, all her friends are astounded that their friend can turn into a weapon and will be going to "the super elite DWMA".
DWMA, of course, has secrets and knowledge which they keep from the general public.