Is she sinful for not making up the Dhuhr and Asr prayers after her purification from menstruation before sunset due to her ignorance of that, and is it obligatory for her to make up those missed prayers since her conversion to Islam, or is repentance sufficient, or is there an expiation?

First: If a menstruating woman purifies herself before sunset, she is obligated to pray Dhuhr and Asr according to the majority of jurists. However, if she only prays Asr, there is no harm upon her.

Second: Abandoning the Dhuhr, Asr, Maghrib, and Isha prayers on the day of purification, and beginning to pray from the dawn of the following day, is a grave error and a significant shortcoming, for which you must repent and seek forgiveness. As for making up the prayers, you are not obligated to do so, according to the more preponderant opinion, due to your ignorance of the ruling; for Allah has forgiven errors and forgetfulness, and He would not punish until He sent a messenger. Therefore, for someone whom the command of the Messenger of Allah (peace be upon him) has not reached, the ruling of its obligation is not established upon them.