Are the prayers and fasting performed by the questioner before learning the correct method of ritual bathing (ghusl) acceptable?

The sufficient (or minimum) performance of ghusl (ritual bath) is the complete coverage of the body's exterior with water, accompanied by the intention. This is sufficient and there is no harm in it. If the sufficient ghusl was not performed, then it is obligatory to make up all the prescribed prayers that were performed after the deficiency in ghusl, until one is reasonably certain that their duty has been absolved. As for fasting, it is not affected by the absence of ghusl and is valid if it is free from anything that invalidates it. Acts of worship are obligatory upon the mature, and it is a duty to learn the rulings concerning individual obligations, such as prayer and purification.