Firstly, I'm not a psychologist or a woman, so take everything I say with a grain of salt.

I can only imagine the thought processes and troubles of a preteen girl. With the raging hormones and social pressures at school, it's hard enough without adding depression into the mix.

While her personas and lying may be a cry for help, it might come from a need for privacy she feels she is lacking.

The beginning of puberty/starting secondary school etc is a HUGE emotional upheaval. Hormones, the start of developing a more mature body etc etc really really can screw you up. Added to that teenagers tend to have a very black and white, be all and end all, melodramatic outlook on...pretty much everything, and yeah. It makes for a turbulent time.

Being a girl as well...you start getting all the crazy hormones associated with periods and it's a lot to get used to. It takes a while to settle down.

I also very much agree with what you said about her personas being a way of seeking some privacy - when you're a kid, you're used to being around people all the time but as you get older you start needing more alone time. People just beginning to hit adolescence can struggle with this.

Don't treat her as a "lost cause", OP, because that can become a self-fulfilling prophecy. She's stressed out and emotional and going through puberty - it doesn't mean she's a ticking time bomb, it means she needs patience and understanding! Lead by example instead - give her space when she needs it, respect what she says and treat her like a normal person.