Is expiation (kaffarah) obligatory for one who broke her fast during Ramadan for several days due to menstruation, then made up those days after Ramadan without knowing that expiation was obligatory, and she does not remember the number of days she needs to make up? And if expiation is obligatory, would it be by paying 15 Riyals for each day, or is there another method?

If a woman fasts the days she missed in Ramadan, then her obligation is fulfilled, and she is not required to repeat those fasts.

As for the expiation (fidyah) for delaying the fast until another Ramadan begins, it is not obligatory for her if she was unaware of the impermissibility of the delay. However, if she knew that delaying was impermissible and she did delay, then she must pay an expiation of feeding one poor person for each day. The amount of food for feeding is approximately 1.5 kilograms of rice for each poor person, and she is not required to repeat the missed fasts.