Are the prayers performed after experiencing a wet dream without ghusl valid if done out of ignorance of the ruling? Is it sufficient to perform tayammum when unable to do ghusl, and what is required regarding the past prayers?

The emission of semen during sleep necessitates ghusl (ritual bathing) by scholarly consensus, due to the Prophet's (peace be upon him) saying: "Yes; if she sees water." Therefore, ghusl is obligatory for one who experiences a wet dream. Otherwise, the prayers performed with ablution while in a state of major ritual impurity would have to be repeated, and they must be made up until one is reasonably certain of having fulfilled their obligation. As for prayers for which tayammum (dry ablution) was performed due to an excuse, they are valid, with the reminder of the obligation to learn the individual religious duties.