To what extent is the circulating message accurate, which states that the brown discharge preceding menstruation is not menses, based on a medical study, and that fasting with it is valid, and that it is safer to perform ablution for each prayer?

What the author mentioned, that the yellowish and brownish discharge, if it precedes the flow of blood, is not considered menstruation, is what Ibn 'Uthaymeen preferred. However, this issue is subject to ijtihad and there is a well-known difference of opinion concerning it. The view of the majority of scholars is that it is menstruation.

As for her statement that normal vaginal discharges do not invalidate ablution, it is incorrect. Rather, the correct view is that these discharges invalidate ablution, even if they are pure.