Is it obligatory for my mother to make up or offer expiation for the days she missed fasting in Ramadan due to menstruation and postpartum bleeding, given that she delayed making them up out of ignorance, and then became unable to complete making them up due to illness? And is it permissible for me to make up on her behalf the remaining fasts?

Whoever breaks their fast in Ramadan must make up for it before the next Ramadan. If they delay it without a valid excuse, they must pay an expiation for each day by giving a mudd of food, in addition to making up the fast. Your mother must make up the days she missed. There is no expiation for her as long as she was unaware of the ruling. If she is unable to make up the fast due to a chronic illness from which there is no hope of recovery, then she must feed a poor person for each day. No one is permitted to fast on her behalf. If she cannot afford to feed, it remains a debt upon her until she can. If she is unable and dies, one of her relatives should fast on her behalf.