Was his assumption correct in invalidating his fast due to the emission of semen during sleep, and what is the ruling on his action of intentionally emitting semen thereafter, and is he considered to have broken his fast on both days, or only on the day he intentionally emitted semen, and what is legally required of him?

Wet dreams during the day in Ramadan do not invalidate the fast; all that is required is to perform ghusl (ritual bath) from janabah (state of ritual impurity). However, masturbation invalidates the fast and requires making up for it. Delaying ghusl from janabah without a valid Shar’i excuse is forbidden. One must perform ghusl to perform prayers on time. If prayers are performed while in a state of janabah, they are not valid and must be repeated. If prayers are not performed at all, that is a grave sin, and the questioner must repent, seek forgiveness, and maintain regular prayers.