Obviously Faith is responsible in the way that she was the one to commit all those acts, but I do think it was a result of her past and her upbringing.
I mean the girl undoubtedly had psychological problems. I mean the basics we know are an absentee Father and a drunken mother who slept around with the worst low-life-scum she could find. And this all when Faith was a lot younger than we saw her. Imagine having all that at age of fifteen? Fourteen? The thought is to horrible to contemplate and it's obvious that she'd be effected by that. And then if you take 'Go Ask Malice' to be canon we also know that Faith found her Mother, currently in the prostitution profession, dead in the back of some random sleazeball's car. If that doesn't create some psychotic issues I struggle to think what would.
Then of course we have the only stable adult figure she could trust- her Watcher. Then she was killed and ripped apart before Faith's eyes by Kakistos. So all that was ripped away from her also.
When she went to Sunnydale, she wished to escape from all that, absorb herself in the life Buffy had created and I think she honestly planned to be a helpful and complete part of it. Her actually turning up at Buffy's house in Amends showed how much she wanted to be part of it, that entire family unit that was the Scoobies. And everything was going well (as well as it can in Sunnydale) but the accidental murder of Finch I think in way sent Faith back a million steps. Everything about the new fresh start she had created fell apart and she went, in effect, into complete meltdown.
Her lying to Giles, saying it was Buffy that killed him, not only reflected her once again unstable mental state, but also her own fears of what people think about her. After being raised around people who thought she was useless and no good, her teachers included, she was afraid that Giles secretly thought the same thing of her and confessing about Finch's death (no matter how accidental it was) would cause him (who we see many times she definitely liked. She defends him to Post, remember?) to reject her as all the adults have before and she couldn't bear that rejection. She saw how they all were Buffy and thought that no matter what they would always forgive *her*, hence why she said Buffy was the one who did it. I'm not saying it was the right thing to do, far from it, but you can understand why.
Her actions of that were all just an extension of all that. She had a psychosis already and The Mayor just seemed to feed that, nurture it in a way until it became out of control. But through it all Faith still desperately wanted that life Buffy had- the life she wished she had as a child. I mean didn't Faith say something like 'You get the Mom, the Watcher, the little scooby gang'? That was always what was behind her actions. Wanting that and believing on some deep scarred level that she could never have it no matter what. That she didn't deserve it. And so she went the opposite way completely, covering up her desires, her fears by saying 'well I didn't want that anyway. I want to be the bad girl' when really she didn't.
I mean in TYG where she kidnaps Joyce, watch that scene in the bedroom. That isn't a raving psychotic- Okay, it is *is* but there's more to it. Playing with Joyce's make-up, bouncing onto the bed beside her excitedly with the mail? That's all the language of a kid playing with their Mom. This is a girl who just wants that stable life Buffy had. And when she rants on about Buffy being too busy with her own life to take care of 'dear old Mom' she's basically saying 'Buffy has this great life, a great Mom and she doesn't even care about you. If I had you as Mom, I wouldn't forget you. I'd see you'.
So, I do believe Faith should be held responsible for her actions- which you have to admit she does in Sanctuary etc in Angel when she breaks down and then willingly goes into prison- but it was some deep-rooted pain going on there. She kept saying it was for the ride, but there was so much more to it. A deep psychosis from her entire crappy life before Sunnydale and a desperate almost obsessive need to fit into the same kind of life Buffy had, but a deep-rooted fear perhaps formed by everyone's low opinion of her in her earlier life telling her that she would never deserve that life and so could never have it.