How can one make up for missed prayers and fasting, given that their exact number is not remembered, and there is doubt regarding the purity of the fasting due to masturbation at that time?

If you practiced masturbation during the daytime in Ramadan out of ignorance, then your fast is valid and you are not required to make up for it. As for making up the missed prayers when ignorant of their number, this is done by investigation. You should make up what you believe, with a strong presumption, will absolve you.