Is it correct to clean oneself after defecating by wiping the place of the excretion with the right hand, and wiping the head of the penis against the toilet wall? What is the ruling on past prayers [performed in this state]? And is it permissible to adopt the view of Ibn Taymiyyah that these prayers do not need to be made up?

The answer includes several points:

1. The prohibition of cleaning oneself with the right hand is due to disfavor (karahah), not outright prohibition (tahreem). 2. Cleaning oneself in a way that removes impurity and makes the area rough is sufficient, but it is incorrect to clean oneself with the right hand. 3. A smooth wall is not sufficient for cleaning oneself because it does not remove impurity. 4. If the cleaning was insufficient and one prayed with an unknown impurity, the prayer is valid and does not need to be repeated. It is permissible to follow this opinion, so there is no need to make up past prayers.