I don't really think the narrator is unreliable. She is very astute in her reasoning. She tells us she would recognize the unknown woman if she saw her in the street.
If unreliable means that she is trying to figure out who the woman was, then yes, we cannot believe everything she is saying. She is trying to figure something out that she does not have the answer to.
We really don't have enough information to answer the question. That being said, I would pick A. She is trying to puzzle out who the woman was and what she was doing there.
King will not testify because he stated to the police that he didn't know Bobo when he was first arrested. The prosecution can prove that King does know Bobo and they will show that he is a liar which would hurt his case.
