Is it permissible for Muhammad, son of Ahmad, to marry the daughter of his paternal aunt, Umm Ibrahim, knowing that his grandmother did not breastfeed any of her children or grandchildren, and that Muhammad's father was not breastfed with Umm Ibrahim?

If your father and your paternal aunt were nursed by the same woman, this does not create a state of mahramiyyah (prohibition of marriage) between you and your paternal aunt's daughter. This is because mere suckling makes them foster siblings, and this does not alter their original blood kinship. Consequently, it does not make your paternal aunt's daughter mahram (definition) to you, and it is permissible for you to marry her Islamically.