This may on may not cover what you want to know, it contains small spoilers for series 3/4 of Charmed.
Paige Matthews (and yes her name her name is Matthews not Halliwell) is the half sister of Phoebe and Piper, and is part witch (on her mother's side) part whitelighter (on her fathers) she was bought into Charmed to replace Prue when she died. She was given up as a baby to protect her (the relationship between her mother and father was forbidden due to him being a whiteligher), she was adopted by the Matthews (who may or may not have been given names I honestly can't remember them though) who were then killed in a car crash when she was 17, the only reason she survived was because she orbed out. With no real family (other than an aunt and uncle) she felt very much alone, but did always feel a connection with the Halliwell sisters, after Prue died Piper cast a 'return a lost witch spell' and found Paige, who in the beginning had a lot of trouble accepting what she was and felt she was living in Prue's shadow, she did however prove herself to be a very competant and powerful witch.
Paige came to FH at 16, a few months after her parents had died, she knew at this point that she had powers, but not that she was a witch (Draco Malfoy told her), she also didn't know Piper and Phoebe were her sisters until Maia (who can see the future) told them. Paige was something of a wild child during her first year (as per her canon teenage years) she drank, slept around and was generally very self-destructive, her relationship with Geoff Chaucer settled her for a while, but when he suggested they take a break she didn't take it very well at all (in fact she turned evil, but this was when I was new to RPing and messed up somewhat) and ended up in the very firey relationship with Sawyer which was no good for either of them and caused her to drink far far too much, until Phoebe finally got through to her, Paige now does not drink, unless one of her sisters actually gives her one. She's now much more together, as she's eager to prove to her sisters that she can be trusted. Oh and she has a tattoo on her back, it's the Charmed Triquetra as shown in the icon.
Being part whitelighter Paige can 'orb' people places, this basically means she can transport herself and 'passengers' somewhere else in the world (or the underworld for that matter), when she orbs it involves her being surrounded by blue lights (orbs) and disappearing, the same is true in the reverse when she arrives somewhere. Like Prue she is also telekinetic, although this also works with her whitelighter power so that instead of just moving things with her mind she 'calls' on object to her by saying it's name and it appears in her hands, again surrounded by blue light. She can also glamour, which means in theory she could look like anyone she wants, in practise at FH I generally just have her change her hair colour at will. Paige is also able to heal, strictly speaking she should only heal magical wounds, but no one's told her this so she'll heal anything. Of course Paige can also write and cast spells, make potions and scry of things, however most the spells she's cast so far have gone very very wrong, due to them being used for personal gain and her not really knowing what she was doing.
And finally Paige can only be killed by a Dark Lighter arrow, but so far this has only come up once, she can be hurt though.
Any questions, stuff you think I need to mention let me know