Disagree, obviously a warped person but very very few women become serial killers. When they do it is usually in cahoots with a man or for profit. She would far more likely become a crack whore or something similar as women tend to internalize.
Although some serial killers have some trauma to the brain, the primary problem is that they have a void in their make up. Whereas others have a conscience, they have none. Many successful people are actually psychopaths as they tend to be above average in intelligence. It certainly doesn't mean they will be murderers though, but they will not hesitate to do so if they find it advantageous sexually or financially.
Psychology is almost by definition subjective. Serial killers, almost to a tee are sexually motivated. There are killers who are hired whose motives are very different than the classic serial killer. Someone who kills for profit is psychologically distinct from those who derive a perverse form of pleasure. It is not really a very complex distinction.
On the contrary, it achieves three very vital things:
This is where you are wrong. Feigning concern about the cost of the death penalty is disingenuous. The appeals process, even in cases which are air-tight and even more readily so proven by dna matches, is something which could easily be disposed of. The Chinese put a bullet to the head of the convicted with no qualms and used to charge the price of the bullet to the family. They no longer ask the family for the price of the bullet, but they've got everything else right.