Is wadi (a thick white fluid that is discharged after urination) impure, and does it necessitate Istinja' (washing the private parts with water) and washing whatever part of the inner vagina it touches, and does water entering the inner vagina invalidate the fast? And what is the outer vagina?

The ruling on wady (pre-seminal fluid) has been clarified in Fatwa (definition) No. 100078. It is not prescribed for a woman to wash the inner part of her private organ when performing istinja (definition)' (cleaning oneself after relieving oneself); rather, she should only wash the outer part of the private organ, which is what becomes visible when she sits down to relieve herself. The entry of water into the inner part of the private organ does not invalidate fasting according to our view, though some scholars believe it does invalidate it because it enters an inner cavity.