Yes, I've read the rules on the first page of this. Twice.
I think as a whole, her main goal is to stop any and all needless death. She has plenty of time on her hands, since she never sleeps, so she constantly works towards this goal - mainly by stopping killers.
She's somewhat backwards in this manner, because she kills killers to stop them, rather then turning them into police or something along those lines.
She hasn't come across anyone like her, or anyone able to stop her - it's pretty hard to hurt someone who can become impermeable - so she's probably freak and it'd turn into an all-out fight if she came across someone who could stand a chance against her who has killed someone before.
With other characters, it depends on what she knows about them. If they've killed someone before, she isn't going to know unless they tell her they have. She'll be plenty(perhaps overly) friendly, unless they aren't friendly to her.
I think weaknesses that could work would be things people who believe in evil spirits use to get rid of them.
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