Is it permissible for me to take my wife back after I divorced her three separate times, then confirmed the divorce twice in front of witnesses, and her waiting period has ended, knowing that the first divorce occurred during a period of purity, and her menstruation followed it, so do the second and third divorces count?

First, attention must be paid to the impermissibility of excessive divorce, as it is a mockery of Allah's rulings.

In your statement: "You are divorced, you are divorced, you are divorced," if you intended emphasis, then one divorce takes effect. If you intended to initiate divorce with all three phrases, or if you had no intention, then three divorces take effect. If the repetition was of the full sentence, divorce occurs according to the number of repetitions. However, if the repetition was only of the predicate ("You are divorced, divorced, divorced"), it is considered one divorce unless you intended more.

As for your statement: "So-and-so is divorced from me by three," if three divorces had already occurred previously, then it has no effect. If it was less and you intended emphasis with the first utterance, then she becomes unlawful for you until she marries another husband.

Your statement in the third instance: "So-and-so is divorced from me by three," has no effect according to the majority of scholars, because it occurred after the cessation of the marital bond. The fatwa issued is based on the majority opinion, and accordingly, your wife does not become lawful for you until she marries another man in a valid marriage and he then divorces her after consummation.