What is the ruling on fasting Ramadan while having masturbated during the day due to ignorance of the obligation of ghusl and making up the fast, and is making up the fast obligatory if one doubts having done it after knowing its prohibition?

You are not required to make up for the days you broke your fast out of ignorance, nor for the days you are unsure if you broke your fast knowingly. As for the prayers you performed without ritual purity (Tahara), the majority of scholars obligate you to make them up. You can find out how to make up for prayers when you don't know the exact number from Fatwa no. 72777.