That said she isn't the most 'stable' person, as she suffers from mild depression, anxiety and OCD, nor is she that...world-wise.
I'm about to give you some very heartless advice...
Red flags buddy. RED FLAGS!!! Depression, anxiety, OCD, homeless, jobless.... that's not a healthy hand of cards to play. This is a situation where you can do some good to help, but you can also set yourself up for a lot of trouble.
You are 17 -- and have a long life ahead of you. Don't confuse 'girlfriend' with 'eternal love' at the age of 17. Do everything you can to help her, but trust your parents when they say "One week." in your house. This can quickly go from a girlfriend who needs some help while she gets back on her feet to a Judge Judy episode...
My suggestion, be there to help her get on her feet. That's your job as the boyfriend. Support her, care about her, help her through the hard times she's in -- but if she fails to make some changes and help herself out of the situation (and leans only on you), you need to draw a line in the sand at some point and walk away. You are just 17 and there are more women in your future; don't send the ship down trying to save her if she won't help herself. Be ready to firmly walk away at some point.
For the sake of complete understanding, my wife is manic (depressive) and yet we've had a happy marriage for over a decade. I'm not saying :"Run away from the psycho!!!" but I am cautioning that you are just 17 and she's your girlfriend. I was 22 when I met my future wife, and 24 when we married... so I'd seen a bit of the world, and my share of girlfriends before finding the one I'd marry. The depression didn't matter because we were both mature enough to see it for what it was and work with it as a team.
Be there for your girlfriend, help her through the hard time, but know when to walk away (when she refuses to help herself, and starts to drag you down). I'm not saying it
will happen but you need to be cautioned
that it can happen and make sure you don't screw up your life in the process!