A: You are correct, in that the provisions of a Will do not establish legal rights before the testator (your father) has passed away. Not until the Testator passes, and after the will is admitted into probate does the will have any legal or binding effect regarding the administration of the Testator's property. The Will can funcion as an advisory prior to death, but again, prior to death and probate, it is not a legally enforceable document.
A: Depending on the size of your grandmother's estate, you need to start a probate proceeding and have yourself appointed as the executor of your grandmother's estate. If her estate is smaller than $100k, then you can avoid probate and handle it via a small estate affidavit. An attorney experienced in probate and estate matters can help you through the process.