What is the Islamic ruqyah for treating infertility, what is the Astaghfirullah group, and how is the ghusl performed with the wudu’ water mentioned in the spiritual treatment?

There is no specific Ruqyah for infertility. However, the way to achieve offspring is through Taqwa (piety) towards Allah, increasing supplication (Du'a), and seeking forgiveness (Istighfar), similar to the supplications of Zakariya and Ibrahim (peace be upon them). Reciting the Quran is a cure; it can be recited over water, and then one can bathe with it. One must be certain that provision is solely in the hands of Allah, and He is the One who bestows offspring or renders whomever He wills barren. This should be combined with taking legitimate means, such as medical treatment and seeking forgiveness. As for the bathing mentioned by the questioner, we do not know of any legal basis for it.