Who inherits the deceased woman in the mentioned case, and is it permissible to perform the Hajj on her behalf if the inheritance is only sufficient to cover the expenses of the Hajj?

The heirs among those mentioned are the sons of her father's paternal uncles, unless the husband's sons are her own sons, in which case they are the heirs and would exclude the sons of the paternal uncles' sons. As for the sons of the sisters' sons, they are considered kin by blood (dhawu al-arham) and do not inherit. Matters of inheritance are complex and critical, and a mere fatwa is insufficient; rather, the matter must be brought before the Sharia courts for investigation and consideration of the existence of other heirs, wills, debts, or rights that take precedence over the rights of the heirs.