We don't yet know anything about Faith's life before she was the Slayer, except that it wasn't exactly sunlight and roses. As the Slayer, she's had a Watcher prior to Wesley who met an unfortunate end and her dealings with the Watchers' Council have been colored by events related to that incident ever since.
She ran away to LA to escape from Wesley and the Watchers' Council, knowing they wanted to send her to Sunnydale and having heard about a half-demon who fought vampires in LA and had managed to stay alive for some years doing so - figuring perhaps they could join forces and maybe she could even learn something.
In LA, Faith accepted a partnership working with Doyle to fight evil. Except she wasn't counting on Wesley following her so determinedly and almost getting himself killed for his troubles. Initially, she wasn't too hot on the idea of him joining herself and Doyle, but she reluctantly agreed that since he was already there and they weren't going to get rid of him short of murder, they might as well all work together.
Faith is currently 17 years old.
This is a slightly different version of Faith than we've seen on BtVS. She's had a hard life, and she's experienced difficult events, but she's still got a little more innocence and cocky enthusiasm left... unless that's just because she's got Wesley and Doyle to run around after her every whim...
Seriously, though, this is a Faith who has had the attention of being THE Slayer right from the start. She's never had to feel second best, and she's never had to share that title or the responsibility, and so she's reacted to it slightly differently.
This Faith loves the rush of Slaying and the fact she can kick anyone's butt just as much as her counterpart, but this is tempered by the fact she knows the last two Slayers went off to Sunnydale following the Watchers' Council's orders and died before they hit eighteen. In this world, there's no veteran Slayer still around in spite of all to show that hey, there's hope yet. The previous Slayers were killed by the Master and his minions and Faith's aware the likelihood is that, one day, so will she be. And this is an eventuality she'd rather avoid; she wants to stick to the fights she has a chance of winning, not become another unfortunate statistic for the Council to shake their heads over.
Faith is an aggressive and enthusiastic fighter, who accepts no nonsense from either of her colleagues and refuses on principle to get involved in the actual business side of Doyle's business. Especially answering the phone. And the less said about her customer relations skills the better.
Initially, her relationship with Wesley was very sour. Over the course of their time in LA, however, those differences have started to get patched up, largely due to Doyle's acting as a mediator in the early days and actually making them stop arguing and listen to each other.
How Faith feels about Doyle remains largely uncertain. He may express doubts as to the fact it's anything deeper than her regarding him as a ready source of food, money, board and sex, but she's certainly rather possessive when Doyle has dealings with other women, such as his ex police partner Kate Lockley.
Quote: “I'm a Slayer. I can take any man, demon or vampire, and if I don't like you I can twist you into a knot so fast that you'll be seeing daylight from the rear.” - City of Doyle
Tammy: “This is a rather different version of the Faith than her counterpart in the regular universe, because she's never had to contend with those issues of being second-best-slayer. That whole Buffy-shaped element has been lifted out of the equation. In its absence, we have a Faith who is more sure of herself as the Slayer but at the same time more aware of the weight of responsibility that role entails.
"Faith still has issues with relationships and commitment, and like her counterpart, she enjoys the violence a little too much and still has that potential to turn down a dangerous road. Unlike her counterpart, she has friends who can try to prevent that from happening, whose attention isn't distracted by other friendships and who are - at least after Evidence of Things Not Seen - in the know about her potential for evil. She has also found herself caught up in a fairly steady relationship with Doyle, which may provide a stabilising influence.”
Ellen: "She has given some subtle indications that she may care more deeply for Doyle than she is willing to admit, even to herself. However, we have also begun to see some hints that everyone who has been truly important to Faith in her life up to this point has been taken away from her, and this may be part of the reason why she refuses to acknowledge that something as fragile and vulnerable as love could ever exist in her life."
Mike: "I think from the first episode Faith was in on Buffy, we
could all see that she was on the fast track to self-destruction. To me, her
greatest problem was that she had all these things happen and all these
emotional issues and absolutely no one to share them with. We'd see her
sitting alone on her bed, watching grainy TV after tragic upheavals, and
everyone knew, 'This girl isn't going to make it as a Slayer.' That's part
of why I only ever warmed to the Mayor as a character after Faith joined him,
since they filled gaps in each other that were missing while she was with the
Scoobies. And yeah, Harry G. cracks me up. ;-)
"But in D.I., Faith has people looking out for her who can actually reach her. Buffy was the only one who ever came close to helping Faith, and their backgrounds were simply too different for them to be able to relate properly. Angel could have helped her, but along came Wes and that big net...Here, Doyle has demonstrated some ability to get Faith to listen to him, and considerable empathy for her problems. And Wes doesn't always act like such a wanker, particularly with Doyle to advise. I think that individually, each of D.I.'s main characters wouldn't last on their own. Faith is the most obvious risk case, but Wes lacks the toughness and judgement that will only come with time, and Doyle is self-destructive in a subtle, but no less severe, way as Vampires, Served Cold showed. Faith can go either way, and I think that the knowledge that she did turn to darkness once (As Doyle learns in Evidence of Things Not Seen), makes it clear to everyone how much of a borderline case she is. Objectively, Angel is probably more about saving souls that Doyle Investigations. But for DI, Faith is the soul that needs saving. Doyle doesn't have Angel's experience with the human heart, but he does know all about sorrow and self-hatred. He provides some much-needed balance in Faith's life, but if that's enough to keep her from going down the same road as her canon counterpart is hard to say."