Are the sticky vaginal secretions, over which urine passes, purified merely by water passing over them, or is it obligatory to perform istinja' from them given that they have been contaminated by urine? And is it sufficient to perform istinja' only from the visible part over which the urine has passed?

Vaginal discharge emanating from the birth canal is considered pure according to the preponderant opinion, but it invalidates ablution (wudu). As for discharge emanating from the urinary meatus, it is impure and takes the ruling of urine.

It is obligatory to remove impurity from urine that contaminates any part of the body, including vaginal discharge. It is not a condition to use the hand; rather, pouring water is sufficient to remove the impurity. However, if it cannot be removed except by hand, then that becomes obligatory. But if only the external part is defiled, then it must be purified without seeking to cleanse what is inside the birth canal.

One must differentiate between pure vaginal moisture and impure madhy (pre-seminal fluid). Madhy is a viscous white fluid that is discharged upon arousal, whereas vaginal moisture is a transparent fluid whose discharge is not linked to arousal. Madhy is impure and requires washing if it touches the body, and it is sufficient to sprinkle water on clothes affected by it. As for vaginal moisture, it is pure. And if you are uncertain whether the discharge is madhy or moisture, the default assumption is that madhy has not been discharged.