If you have parental permission, yes, you can.
Not legally
Yes.
Not legally.
You should consult an Lawyer in Missouri and he will guide you to how legally take adult guardianship.
18.
get an alibi
Yes
Legally she cannot leave home. Until she turns 18, her parents are responsible for her and decide where she can live.
Why would you do that to your daughter?
Yes.
No.
No, in order to leave your parents or legal guardian in the United States you must be at least 18 years old. Although the law in Missouri has some twists, but i belive in your situation the answer is no.