I absolutely do not believe that anyone is ever "possessed".
There is a wide range of different types of mental illness; and, of course, some particularly serious mental illness includes behavior or thinking that could mimic what we see in horror movies about "possession". At the same time, many people with mental illness show no signs of any such behavior or thinking.
Regardless of which type of mental illness someone has, there is a scientific explanation and process to mental illness. There is nothing "magic" or "possessed" about it.
Serial killers aren't even always mentally ill. Many are, instead, sociopaths; which means they lack "conscience" and the ability to feel empathy for their victims. It has now been shown that there is a part of the brain (associated with conscience and feeling empathy) that may not be developed in sociopaths.
In the 1600's, the Salem Witch trials resulted in the murders of innocent people believed to be "possessed" and "witches". One of the contributing factors to the "witches" myth was that some people and animals had suffered health problems like seizures and hallucinations. Because of the religious beliefs of the people at the time, there was talk of "possession". It is now know that people were infected with a fungus that had grown in the rye crop because of weather conditions. (Rye was a staple in their diets.) Again, whenever there is behavior or thinking that one might imagine as "appearing possessed" there is always a scientific, "non-magic", explanation for it.