Is soap considered essential for removing impurities, what is the wisdom behind washing a vessel licked by a dog seven times, one of them with earth, and is it permissible to perform ablution in a sink that has been used for Istinja' (cleaning oneself after defecation or urination) or for cleaning children's impurities?

Using soap to remove the smell of impurity (najāsa) is recommendable, not obligatory, if the impurity cannot be removed otherwise. The jurists explained the hardship that necessitates excusing the smell of impurity as requiring something other than water, such as soap. As for the wisdom behind washing the impurity of a dog with earth, it has been said that it is a matter of devotion (taʿabbudī). It is also said that a dog's saliva contains germs that can only be removed in this manner. If what is meant by "the sink" is a basin of flowing water, then there is no harm in performing purification (ṭahāra) in it after removing the impurity and pouring water over it. However, if water is not poured over it, then performing ablution (wuḍūʾ) in it is disliked.