When should one fast and pray, or abstain from them, given the intermittent menstrual bleeding of varying colors (yellow, beige, brown, black, red) throughout the month, with the yellow discharge sometimes continuing until the next period?

First: The yellowish or brownish discharge that precedes menstruation or appears after purity is not considered menstruation. However, the yellowish or brownish discharge that appears after the onset of blood and before purity is considered menstruation. Black blood, red blood, and the yellowish discharge that follows them are considered menstruation until the sight of the white discharge (al-qassah al-bayda') or complete dryness.

Second: If the blood, or the yellowish and brownish discharge that follows it, extends beyond fifteen days before seeing the white discharge or complete dryness, then you are in a state of istihadah (non-menstrual bleeding) according to the majority of scholars. Some scholars are of the opinion that istihadah is not established unless this continues for most of the month, and this is closer to the evidence. In the case of istihadah, you act based on your previous habit, so you perform ghusl after your usual menstrual period and perform wudu for each prayer, or you differentiate between the types of blood if you do not have a regular habit. It is recommended to consult a doctor to address persistent discharges.