Is it permissible to make up the prayers from the age of sixteen that were performed without covering the 'awrah, before making up the Dhuhr prayers from the ages of thirteen, fourteen, and fifteen?

Prayer is not obligatory before puberty. The questioner must calculate and make up for the prayers she performed after puberty without purification or covering her 'awrah, because they are a debt upon her. She must repent from intentionally neglecting a condition of prayer. If she was ignorant of the ruling on covering the 'awrah, then there is a difference of opinion regarding the obligation of making up those prayers, but it is more cautious to make them up.