What is the ruling regarding the prayers I performed after taking a ritual bath (ghusl) from major impurity, while doubting whether the water reached my face during the wash?

Your sitting under the shower and letting water flow over your entire body is sufficient for the validity of ghusl. There is no condition to wash the face or each limb separately, nor is rubbing (dalk) obligatory according to the most preponderant opinion. It is sufficient to have a strong presumption that water has reached all parts of the body. There is no need for doubts and whisperings (waswas); you should disregard them.