Setting: late 1880s/early 1890s London, England
It's a pretty specific set of questions, unfortunately: how would a woman, middle to upper-middle class, be viewed if she went to a public library? Alone or with a male relative?
As for university, I know at this point women were going to and graduating from universities (not many, but they existed), but there's precious little about how they were expected to behave there or how they were treated (I can hazard a guess, but any specifics would be nice), or how they were viewed by the public at large.
Given that the female character is trying to find information about demons, might she be better off going to a friend of the family that is interested in spiritualism, or possibly the church? (She's trying to avoid that particular route.)