Does the involuntary emission of semen after Fajr prayer invalidate the fast, render the prayer unacceptable, and prohibit touching the Qur'an?

If semen is emitted merely by thinking, the fast remains valid. However, if it is emitted due to masturbation, the fast is broken, and that day must be made up, along with repentance to Allah. Regarding the Fajr prayer, reciting the Quran, and touching the Mushaf, none of these are permissible until after performing the ritual bath (ghusl) from Janabah (ritual impurity).