Your granddaughter's behavior suggests she is in need of either individual counseling or treatment in a residential facility. Teenagers who act out like this are rebelling against something - typically the environment in which they are living. This behavior *always* comes from something -- it is never "random" or for no reason. Teens act out their feelings - you can tell what their life is like bu how they behave. It sounds out of control to me.
As to what her thoughts and feelings are - it seems that she is mirroring disrespect. When teens feel disrespected, they behave that way.
Of course she is responsible for her behavior, but it's time for a parent to really step-up and either put her in weekly individual counseling with someone who specializes in teen delinquency, or find a residential treatment program for her for awhile - they teach all the things kids need to know to do better in their life.
The psychiatrist has a diagnosis ... do you know what that is? That will tell you if he/she is treating Jess for Depression, or Bipolar (or what ever their evaluation concluded).
This is clearly on unhappy child. If anything, she needs someone who can give her unconditional support... I hope that can be you. Speak with her and tell her that her behavior is upsetting, but she, as a person is very much loved, and that you want to be there to help her in any way you can. Maybe she will open up to you.
I wish you the best of luck,