Is it incumbent upon my sister to make up only 8 days or the entire month, in the event that she broke her fast for 8 days from the beginning of Ramadan, then performed ghusl, and yellowness persisted throughout the entire month?

Yellowish or brownish discharge is considered menstruation if it occurs during the period of a woman's regular menses; otherwise, it is not considered menstruation. Therefore, your sister must make up the eight fasting days she missed. As for the yellowish discharge, she only needs to make up the days that coincided with her regular menstrual period.