Do brown drops before menstruation count as menstruation or not, and is expiation required for intercourse that occurred under the assumption that it was not menstruation, and for whom is the expiation?

Yellowish and brownish discharges are considered menstruation if they occur during the customary period or if they are connected to blood at its end. If your wife sees these drops during her customary period, then it is menstruation, and intercourse must be avoided. Otherwise, there is no sin upon either of you for it. As for past intercourse during the yellowish and brownish discharge period, there is no expiation required from either of you, as you both presumed it to be a state of purity.