Is the white discharge considered a sign of purity from menstruation if it is accompanied by a drop of blood or a small amount of it? And is ghusl (ritual bath) obligatory in this case, or should one wait until the white discharge appears completely free of blood?

If you see blood mixed with white discharge, this is not a sign of purity [tuhur]. Purity from menstruation is only achieved when the blood stops, and it occurs through one of two signs: dryness or the white discharge (al-qassah al-bayda’). So, if the blood, yellowish discharge (sufrah), and brownish discharge (kudrah) have ceased, then you are pure, whether white moisture appears or not. Therefore, as long as the bleeding continues, you are still menstruating. If you see purity by one of its two signs—dryness or the white discharge that is not accompanied by blood—then you are pure and obligated to perform ghusl and pray.