How is the estate of a deceased paternal aunt, who has no sons or daughters, to be distributed, given that she has gold, houses, and agricultural lands, and what is the share of her brothers' sons and daughters?

Your aunt's brother's sons inherit the estate by ta'sib (agnatic inheritance), while his daughters do not inherit because they are from dhawu al-arham (relatives through the womb/uterine kin). It is commendable to give them something from the estate. Inheritance cases must be referred to the Sharia courts to verify all heirs, wills, and debts before distributing the estate.