Is it obligatory to perform ghusl and pray upon seeing light brown discharge at the end of the menstrual period, and is it obligatory to make up for the prayers missed during that period?

What you see on the last day, if it is blood, then it is menses. If it is dirty water, then it is a brownish discharge. The brownish discharge is considered menses as long as it is connected to blood. Do not perform ghusl until the discharge stops and you see purity by one of its two signs: dryness or the white discharge. So, when you see purity, you must hasten to perform ghusl. You do not have to make up the prayers you missed during the time you saw this discharge, because it is menses.