Father passed away about 30 days ago. He was married but separated for at least 15 years. (not legally). As his daughter, can I start the probate

Anyone can apply to be appointed administrator (no will) or executor (with a will) for any probate estate. If that application is contested, the Court will hold a hearing to determine who the best person is to administer the estate. You don't have to wait for anyone's permission to file the application.   On the other hand, if ALL you're looking for is to claim life insurance policies, then you may not need to open an estate at all. Contact the life insurance companies and report his death, then comply with their requests for information. All they should need is a death certificate and some of their forms filled out and they will start making distributions to the named beneficiaries.