While the property is in probate and it is listed as estate of him, should that tax reduction remain until the estate is closed?

I am the executor of my father’s estate per his will and I have been appointed the personal representative through the probate court in South Carolina. Fortunately he did not leave many debts other than a mortgage payment (approx. $13,000), and a car and motorcycle notes. I am in the process of establishing an estate bank account. I have two questions. 1. Can I rent the house? If so my plan is to place the rent funds in the estate account and continue to pay the mortgage/taxes/insurance from those funds plus any other unknown debts that come up from the notice to debtors I listed in his local paper. 2nd question: He was 100% service connected disabled therefore paid reduced property taxes on the home. While the property is in probate and it is listed as estate of him, should that tax reduction remain until the estate is closed? Thank you for your time.