I want to disagree that Faith is a psycho. By psycho I'm guessing that you are referring to a psychopath. Faith clearly shows the symptoms of being a psychopath in s3, but because she shows remorse in later seasons, she by default is not a psychopath. I think Faith's situation is very complicated. I'm not condoning her actions, but she did go through a lot which led her to get ticked off, this could happen to anyone in the right circumstances. Because change occur, her delinquency was not due to psychopathy, even if she demonstrated psychopathic symptoms. It is possible to be a killer without necessarily being a psychopath. In the case of Faith, because she never had a support system, I'd lean toward the fact that she never learnt to differentiate from right and wrong behaviours, a classical delinquent characteristics, which made it easier to flip. The mayor bringing in that structure that she was lacking would have meant that she could very easily be manipulated into fallowing the mayors ideology. We studied those type of behaviours in neuroscience, and although I may be wrong, that is my take on her behaviours.
Now for Buffy and Faith, I do think Buffy still sees some humanity in Faith, it was demonstrated on a multitude of occasions in s3 in the leading to the events where Buffy almost kills Faith. When in the hospital, it is clear that Buffy still has love for Faith. My memory is a bit fuzzy on the exactitude of the church scene, but at that point Buffy has every right to despise Faith, I don't think that means there isn't this one tiny part of her that still believes Faith could make a 180 turn. In s7, I actually find Buffy very forgiving of Faith, I don't think she ever entirely lost that feeling that Faith had humanity left in her.