Is the fasting and prayer of an unmarried woman who experiences intermittent spotting due to a menstrual cycle disturbance valid, and is it permissible for her to fast on the 9th of Dhul-Hijjah in this state?

If the total blood flow amounts to a day and a night and does not exceed fifteen days, then it is menstruation (hayd), which necessitates refraining from prayer and fasting. The purity that occurs intermittently within the menstrual period is valid purity. However, if the total blood flow is not suitable to be considered menstruation, then it is irregular bleeding (istihada), and it is permissible to fast and pray with it, though ablution (wudu) is required for each prayer after its time has begun.