Is an increase in the number of menstrual days due to an IUD considered Istihada (prolonged non-menstrual vaginal bleeding), and is ghusl (ritual purification bath) required after the appearance of a light brown discharge following ghusl?

If the bleeding exceeds the duration of the menstrual period, and is continuous with it, having the same color and smell, and does not exceed 15 days, then it is menses (hayd). However, if its color or smell differs, or its duration exceeds 15 days, then it is irregular bleeding (istihada). In this case, you should perform ghusl after the duration of your usual period and perform ablution (wudu) for each prayer. As for yellowish or brownish discharge after purification, it is not considered anything.