Is it permissible for a woman to fast and pray if blood continues to flow for two days, then turns into light brown discharge mixed with white?

What you describe as brown discharge that appeared after the blood and before dryness or the white discharge is considered menstruation. Therefore, do not pray or fast during its presence, due to what was narrated from Aisha, may Allah be pleased with her, that she used to tell women: "Do not hasten until you see the white discharge." Thus, any yellowish or brownish discharge a woman sees after blood, before purification, is considered menstruation. Purification occurs either by the dryness of the private parts from blood or by seeing the white discharge.