So...you think it's BAD that Buffy wants to pay for taking a person's life - even accidentally - and make amends? Is that what we're talking about here?
I think you have a really low opinion of Buffy.
Anyway, yes, I think it is exactly Buffy's natural reaction to turn herself in when she accidentally kills someone - there's a precedence for this, when she 'killed' Ted, she was devastated, horrified of her actions, and when the Deputy Mayor was killed, she felt the same thing. Buffy wasn't even responsible for that and she still felt an enormous amount of guilt, guilt that she couldn't handle and so went to Giles to try and do something about it.
So, yes, I think it was Buffy's natural reaction to an accidental death she thinks she's responsible for. An accidental death that was purely accidental? No, I don't think she would have turned herself in. But within the confines of the spell, Buffy would have been 100% responsible for Katrina's death - if Katrina hadn't already been dead. Andrew didn't mess with Buffy's emotion's, he didn't do anything to Buffy's actual mind or memories or emotions, he just manipulated time and space in order to confuse Buffy enough to think that she had killed someone.
As for Spike, as LOATH as I am to admit it, he did have a point. Buffy handing herself in and going to prison would have left the world defenseless. Two Slayers behind bars is not what the world needed.
But beating Spike up didn't really have anything to do with the situation at hand. He was trying to stop her making a choice, and Buffy couldn't deal with that. She had already had one choice taken away from her (Willow bringing her back to life despite it being Buffy's choice to die) and she didn't want Spike to do the same thing. She beats him so that she can do what she thinks is right, whether it's the right decision for the world at large or not, it's still the right decision for HER. So she lays into Spike for trying to make up her mind for her and it devolves into her self-loathing over the fact that she's sleeping with someone she considers a monster, something she hates herself for. Once Spike isn't in a position to stop her, she leaves him and goes to the police.
It's only after she finds out the girl's name does she realize that something isn't right. I think she still feels responsible for Katrina's death, though, in that she should have stopped Warren sooner.