Is it obligatory for a woman who intended to make up for one day she missed in Ramadan due to menstruation, and then her menstrual period began on the same day of making up the fast, to make up for one day or two days?

A woman is not obligated to make up for the days she missed in Ramadan due to menstruation, except for the original days she missed from Ramadan. For making up missed fasts is a substitute for what was missed in Ramadan, not a new, independent obligation. Whoever breaks their fast during a makeup fast for Ramadan is only required to make up for one day. This was reported from some of the early Muslims and was mentioned by Ibn Hazm in "Al-Muhalla" and in "Al-Taj wa Al-Iklil."