How can a woman determine her state of purity if her menstrual cycle is irregular, and it is followed by continuous discharge of yellowish and brownish直到the next menstrual period, and she rarely sees the white discharge (al-Qassah al-Bayda’)?

If the yellowish discharge is continuous and does not cease after seeing menstrual blood, then the clear blood is considered menses, and anything else is irregular bleeding (istihada). You should perform ghusl (definition) after the clear blood ceases, then perform wudu for each prayer, and pray your fard and nawafil prayers with that wudu until the time for the prayer exits. You will have the rulings of ritually pure women until blood reappears.