Are the prayers of the questioner valid since reaching puberty, taking into account that she was not performing the ritual bath (ghusl) correctly after menstruation, nor was she intending a complete ghusl, and she predominantly believes that the water was not reaching all parts of her body?

For ghusl (ritual bath), it is sufficient to circulate water over the entire body without requiring certainty; rather, a strong presumption is enough to alleviate hardship, and doubt after completing the act of worship has no effect. Rubbing the body during ghusl is mustahabb (recommended) but not wajib (obligatory) according to the majority of scholars, and water reaching the body without rubbing is sufficient. Rinsing the mouth (madmadah) and inhaling water (istinnshaq) are wajib according to the Hanafis and Hanbalis, and sunnah (recommended) according to the Malikis and Shafi’is. If they are forgotten, they can be performed later because continuous sequence (muwalat) is not obligatory in ghusl. It is not obligatory to remove earrings; merely moving them to allow water to reach the earlobe hole is sufficient according to some scholars. Others hold the view that the earlobe hole is considered part of the inner body, thus it is not necessary to ensure water reaches it.