What is the ruling on doubt after purifying impurity? And does certainty of impurity fall away from the mukallaf (a person responsible for religious duties)? And what is the ruling on doubt concerning the purification of the place of defecation?

The cure for waswasa (obsessive whispering/thoughts) is to ignore and disregard them. Doubting the purification of impurity after finishing has no effect. What is obligatory in istinja' (washing after relieving oneself) is to pour water on the impure spot until one is reasonably certain the impurity has been removed. Reasonable certainty is sufficient, and absolute certainty is not a condition. If you doubt that impurity from the toilet has affected you, do not pay attention to the doubt, and do not make a judgment based on it unless you have certainty. If you are certain that a specific spot has become impure, wash it by pouring water on it.