Is what I did considered correct in abandoning prayer and fasting upon the appearance of brown and yellow discharges after a delayed period? And is ghusl obligatory despite the continuation of these discharges? And what should I do regarding menstrual cycle irregularities?

Brown and yellow discharges are a matter of scholarly disagreement regarding whether they constitute menses. The preponderant opinion is that they are not menses as long as they are not preceded by blood. If the worshiper prays and fasts, she is not required to perform ghusl thereafter unless she sees blood. If she follows the opinion of those who consider it menses, there is no harm upon her, and she must perform ghusl after its cessation and refrain from fasting and praying. In all cases, she must make up the days she missed fasting. Any blood seen by a woman during a time suitable for menstruation is considered menses.