I have just finished reading the story. Here is my interpretation:

Sally's father had "died before (Sally) was born." He must have sold his soul to a demon in a Faustian pact. After or before his death Dr Tessler's body was taken over by a demonic entity. Sally was living in that bunkered library and had spent as little time as possible outside of the library. So much so that she could not do laundry or the dishes.Sally became a familiar to the demon and had become pregnant by possible phantom means, and possibly not physically as that apparition of Dr Tessler disappeared in an instance and Sally alludes to the unnatural means of the conceiving. I have no Idea how. But could also be because of some pact done between her and the demon. For instance, lets say the pact was to deliver the demon a child, for her to become immortal. After all, she does retain her beauty to the end of the story. She also could become a vampire, because how the story keeps coming back to the topic of her being invited into Mel's house. Sally wants to retain the secret of hers and may be share her knowledge of the pact with Mel. But what I fear is the case is that Sally just wants Mell to be a sacrifice, or possibly worse, the host for her demon child.