What is the ruling on water splashing from a Western toilet bowl during istinja, and is it obligatory to purify areas that water does not reach by flowing down to the ground?

The water that splatters during istinja’ (cleaning oneself after defecation/urination) is originally pure, unless it changes due to impurity. If it changes due to impurity, then whatever it touches on the body must be purified. What is mentioned is a form of waswasah (religious obsessive-compulsive disorder), and for istinja’ and purifying impurities, it is sufficient to have a strong presumption that purification has occurred, to remove hardship. It is stated in Manar al-Sabeel: "And purification with water means the return of the roughness of the area to its previous state, and a strong presumption of it is sufficient, to remove hardship."