Does the inherited leased property count as an estate, and is the paternal aunt entitled to claim it after the grandmother bequeathed the property to her father and gold to her?

Your grandmother's bequest to her son and daughter (your father and your paternal aunt) is considered a bequest to an heir, and it is invalid unless the heirs accept and uphold it. If your father and your paternal aunt accept this bequest and are content with their shares, then neither of them has the right to demand anything from the other regarding what was specifically allocated to them. Therefore, if your paternal aunt agreed to the bequest while she was an adult, mature, and of sound mind, then she has no right to demand anything related to the aforementioned shop. It is preferable to refer this matter to the Sharia courts for consideration.