What is the ruling on one who masturbated during the daytime in Ramadan intentionally, and fasted to make up some of the days, but then forgot whether he had made up all the days or not? And does expiation (kaffarah) result from that?

Masturbation is forbidden. Intentionally doing it during the daytime in Ramadan invalidates the fast if it leads to the emission of semen; otherwise, it does not. You must make up the days that you are certain were invalidated, but you do not have to make up those about which you are doubtful. If you are certain a day was invalidated but are unsure if you made it up, then you must make it up. No fidyah (expiatory payment) is required for delaying the make-up fast due to the legitimate excuse of the menstrual cycle continuing.