You aren't going to get a very good mark in your epq quoting random people on Mumsnet's opinions. You need to be quoting actual academic research from books and scientific papers. May I suggest you first google how to write and research an essay, and critically assess evidence, if you haven't been given any guidance.
Horizon (BBC) has a couple of interesting documentaries about psychopathy that you might find a useful, easy starting point. One of them covers the interesting case of a neuroscientist, James Fallon, who was examining images of (convicted) psychopaths' brains and discovered that he had the same "brain differences". He also has a gene known as the warrior gene that predisposes people to violence. He then found out from his mother that he was descended from a murderer. There is evidence that psychopathy is a neurodevelopmentmental disorder, ie nature, and that certain genes predispose people to behave in certain ways, however, there is also evidence that nurture also plays a part. James Fallon grew up in a loving, supportive family. He believes that that helped him to use his psychopathic traits to succeed professionally rather than go down the path of a criminal lifestyle.
Of course, James Fallon is a sample size of one (so you can't really draw conclusions from that), so you would need to look for larger studies that investigate the hypothesis that nurture influences whether people can overcome natural psychopathic tendencies. An alternative theory would be that James Fallon also has genes that give him a high IQ (nature). Could it be IQ that influences whether psychopaths become criminals? Or are IQ AND nurture BOTH factors that influence outcome?
Not all serial killers are psychopaths though but that is one small pointer to get you started.