Can my sister purchase our parents property in estate that has not been probated without my knowledge and then sell it without my knowledge

First, your father's estate must be probated by a Court heirship proceeding, small estate affidavit or Affidavit of Heirship, passing his interest to your mother (if all his children are her children). Second, if your mother lacked legal capacity to contract when she "sold" the lots to your sister, report elder exploitation to Adult Protective Services. Third, if the person who purchased from your sister did not know all this, your remedy is to sue your sister for the money she got from selling the lots. You may be eligible for free representation through Volunteer Legal Services or discounted representation through the Modest Means program of Lawyer Referral Service in your area or through a clinic at a nearby law school.