What is the ruling concerning prayers performed in a previous period while ignorant of some of the rulings on purity, and how can their number be estimated for making them up?

If you perform a full-body ablution with water, intending it as a ghusl to remove janabah (ritual impurity), then your ghusl and prayer are valid. Uttering the intention verbally is not a condition. As for praying with impurity out of ignorance: if someone prays while affected by an impurity that is pardonable due to ignorance or forgetfulness, and then realizes it after the prayer, some scholars believe redoing the prayer (qada') is obligatory, while others do not. If the opinion for obligatory redoing is adopted, then it must be done according to one's capacity and what is most likely sufficient for the number of missed prayers.