Are the thick, opaque, white or yellowish discharges that have an odor considered pure vaginal discharges that do not necessitate istinja (washing the private parts with water)? And does al-wady (a thick, white, cloudy discharge that exits after urination) only come out after urination?

The aforementioned discharges are considered vaginal secretions, unless they are yellowish or turbid, in which case they have their known rulings. Yellowish discharge is a color like light blood or egg yolk, and it can be the color of the date palm spathe or figs. Wadi (seminal fluid) is a whitish, turbid, often thick liquid that usually exits after urination or when carrying something heavy.