Overturning adoption/restoration of parental rights?

No, but if they think you're a suitable parent, they can give you custody.

Is this just teenage rebellion, or is there a possibility that there is something medical going on? If it's medical, can you handle it?

No, you have no legal rights, and just because she was adopted does not mean that she is having these issues. Her hormones are going crazy, and unfortunately she is one of those kids that has a hard time with it.

My cousin was put into a juvenile detention center when she was 12 (13 now) due to trying to commit suicide about 15 times, and with that she was in and out of the hospital with more health problems then you could imagine because of the stuff she put into her body. The final straw that landed her in juvenile detention was when her mom called the cops because she was threatening her mom with a knife, and when the cops showed up she would not put the knife down. She was sentenced to 6 months, but now that it has been 5 of those months, whenever she has a good day it is accompanied by 2 bad ones.

She was not brought up in a bad situation, shes always lived with her mom, step dad, and her two brothers, she has a lot of contact with her dad, and her other brother, and a extended family structure of people who don't have any issues. We are here to support her, and I hope she does not have to spend her teen years in Juvenile hall, so I just don't know.

I am sorry to say but if your daughter was truly kept from you for 12 years, then there is obviously a reason for it. Things like that don't happen for no reason. Be fortunate that she is in contact with you, and maybe you can be a good role model for her in the coming years when she needs a friend the most.

No. However, they can choose to make you her guardian. Really, it sounds like they are having a lot of teenager issues with her. You are just a cool new introduction into her world. It doesn't mean that she will do better for you than for them. However, if they are willing, work out some arrangement. I also don't believe her garbage that she attempted suicide to get away from them. If she attempted suicide, it's possibly because she is bipolar or suffers from depression.

No you have no legal rights.

They don't just put kids away for being unruly. She's12 & has already attempted to hurt herself, she needs professional help. You should worry about her getting the help he needs, don't feed into her fantasies.