What is the ruling concerning my sister's fasting, given that she is accustomed to eating stones every day, and is she required to make up the days on which she ate stones?

Swallowing a small pebble invalidates the fast according to the majority of scholars, because it is not something ordinarily eaten. Therefore, the woman mentioned must fear Allah and preserve her fast from what invalidates it. She must also make up every day in which she invalidated her fast. It is unlikely that a sane person would intentionally eat, except if ill.