Generally, property valuations change as a result of sale or improvement (or lack thereof). On occasion, some states such as TX have an annual reappraisal so you must be on your toes each year. The death of an owner is not generally thought to be the reason for a change in valuation.
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Most likely yes given your facts above. The previous poster is correct that valuations could change based on sale or transfer of property. Elderly individuals also typically get valuation freezes for "Over 65" in addition to the general homestead discounts. You would need to discuss all financing options with the current mortgage company
You do not mention anything about any probate administration on your grandfather's estate. Some type of probate will have to occur. As to the property taxes, they will most certainly go up on House (1). The loss of the over 65 exemption and the homestead exemption will result in higher taxes at the same appraised value. The appraised value could easily change, up or down, each year. House (2) did not have those two tax exemptions so those property taxes will only change if the appraised value changes. As to the mortgage, the lender will accept payments from anyone. If payments are not made, the lender cannot foreclose without notice and in some cases permission of the court in which the probate proceeding is pending. You are not personally obligated to pay the mortgage unless you assume liability. You may or may not be able to sell House (2) quickly depending upon the type of probate proceeding that occurs. You will have to be represented by an attorney in that probate proceeding and that attorney can address these issues specifically.
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