The way I see it, Faith is more spooked by her own callousness towards killing a human, and the Scoobies reaction to her actions, than the murder itself.
She's scared for herself, and the serious God complex she's developing, and the apparent result of her Slayer philosophy.
I don't think so. Faith's initial reaction is that she is badly shaken, trying to keep Allan alive, saying (correctly) that she didn't mean it, trying to wash the blood off the hands, etc. It is only after Buffy's bizarre reaction that Faith's attitude hardens to I don't care. I think that by that time the damage was done. When Buffy thought that SHE had accidentally killed a human (Ted), none of her friends were screeching that being a slayer wasn't the same thing as being a killer. They supported her and tried to help her through it, and they didn't have the first hand knowledge of making the instantaneous decisions that a slayer must make that Buffy had. She should have calmly suggested that they go to Giles for advice, as this sort of thing surely must have happened to slayers before (and in fact, it looks like the Council did have procedures for dealing with this sort of thing).