Are the brown or yellow discharges that appear after menstruation, differing from it in form, color, and odor, considered part of the menstrual period, or are they not considered menstruation and require special purification?

Yellowish or brownish discharge after the cessation of blood and the sighting of purity is not considered menstruation, unless it is connected to the blood or occurs during the usual period. It is obligatory to perform istinja (cleansing) and wudu (ablution) for prayer from it. If it continues throughout the day, then your ruling is the ruling of one with incontinence.