Must one perform ghusl again for the emission of semen, and what is the ruling on the fast of that day, if the intention for ghusl was only purification from menstruation and one forgot the intention of purification from semen?

Your ghusl (definition) (ritual bath) is valid, even if you had forgotten about the state of janabah (definition) (major ritual impurity) due to seminal discharge. This is the opinion of some scholars, and you are permitted to follow this view. This is because a lay Muslim is allowed to follow a scholar whose knowledge and piety they trust, and they are not obligated to adhere to a specific madhhab (definition) (school of thought). As for whether your fasting is accepted or not, that is a matter of the unseen, known only to Allah.