Is a menstrual period considered to be such if it starts with very light red spotting on the first day, then turns dark brown on the second day, then becomes red again on the third day? And is fasting obligatory in this situation?

As long as you have seen blood and have not seen purity, then you saw a brownish discharge connected to the blood, then this brownish discharge is considered menses. Therefore, you are menstruating; you should not pray or fast until you see purity, by one of its two signs.