Schizophrenia is a possibility like you said, I also turned out to have it for example but bipolar disorder and even major depression for example can also cause people to hear voices.
I had a friend that had some of those symptoms. It turned out she had schizophrenia.
I would say if you feel these voices are coming from outside yourself, you should speak to a psychiatrist. I do not know about the other behavior, but feeling someone else is speaking to you directly inside your head, (or only to you from ourside your body, type of thing,) that is an indicator that you should see a psychiatrist. There is help out there and it is better to ask for help than to suffer alone.
I used to have this voice that obsessively said it was trying to steal my soul for roughly ten years straight. I assumed it was supposed to be satan and I don't even follow Christianity and that still didn't make it go away. Then I took antipsychotics and it went away but then random voices came about instead when I am tired or stressed or relapsing or sometimes randomly when I am not keeping my mind busy.