Is it necessary to make up the days during which you experienced what you suspected to be a brownish discharge after a long period of purity, or when you were unable to ascertain due to the lighting, knowing that your usual habit is for menstruation to begin with a brownish discharge, and is it considered dryness if a brownish discharge appears moments after checking and seeing nothing?

You are not required to make up for the two days, because doubt concerning menstruation has no effect. Things are judged to remain in their original state until the contrary is certain. If you are certain that the brownish discharge appeared during your customary period, then it is given the ruling of menstrual blood.

As for a valid state of purity, there must be a period of time, even if only an hour. Seeing brownish discharge moments or minutes after the spot becomes dry is not considered purity. So, if she becomes pure during her customary period, she should perform ghusl (ritual bath) and pray. Whenever she sees purity, she is pure, and there is no distinction between a short or long period of purity.

It appears that purity lasting less than an hour is not considered purity, unless she sees something that indicates it, such as her bleeding stopping at the end of her customary period or her seeing the white discharge (al-qassah al-bayda').