Must one make up the days of Ramadan in which masturbation occurred without knowing the ruling, and what is the ruling on the prayers performed during that period?

Masturbating does not invalidate the fast nor necessitate ghusl, unless one is certain that semen has been discharged. If semen is discharged during the day in Ramadan and the person is ignorant of the ruling, then their fast is valid. As for neglecting ghusl due to ignorance when it was obligatory, there is a difference of opinion among scholars regarding the obligation to make up the prayers, but the more cautious approach is to make them up.