Why does Cathy kill her parents and what does she have to do with her Latin teacher's death?

She's a sociopath. She has no sense of right and wrong, and she does whatever she does for gain, whether it's of material possessions or of freedom. I don't remember the Latin teacher, but as a young adult she also poisons the madam who has treated her like a daughter and inherits the woman's establishment. I'll have to look up the teacher!