I don't know the law in Pennsylvania, but generally speaking all the things you are holding onto, as well as information about the family circumstances and history of violence, will be very relevant to the court. If he does get a paternity test he will have to pay child support, but his family history and circumstances may preclude him from getting custody. However, he may be entitled to visitation (possibly supervised by an officer of the court or other neutral party.) Certainly if he has ever been violent toward you, you should make sure you have police reports on that.
You may still be able to move even if he proves paternity - there are plenty of people who have children that live in other states. I don't think they can force a minor to be emancipated from her own parents and live away from them, just for visitation to a non-custodial father.
Some states do take grandparent's rights very seriously, so it may be possible for the grandmother to get visitation if paternity is proved. That really depends on state law, and some of it is the judge's discretion.
Generally speaking, I would say take all the documentation to your lawyer, and ignore everything the father says and does. Do not reply in any way if he texts or calls you, and don't talk about it to anyone outside your immediate family. If he is from a manipulative and abusive home, he will use anything you say to keep you caught up in his drama. Just ignore him and be patient with the legal process. He is saying those things to hurt you and provoke you, because that is what he has learned from his family as a way to control people. If you respond in any way you are stuck in his game.
And if you don't feel like your lawyer is working hard for you, or supportive of your best interests, find another one. Not all lawyers are equal, and it is a relationship that has to have good communication.