What is the ruling on searching students to ensure they do not have cheating aids with them, and on exaggerating in this by making them remove their shoes and some of their clothes, and is it permissible for the searcher to ask the student to remove his underwear to look for cheating papers?

These matters are not judged by a general rule; rather, each case refers to its specific details and circumstances. That which does not entail a religious prohibition, such as the exposure of 'awrah (private parts), may be done to achieve the slightest benefit, and it does not require necessity or urgent need. However, that which entails a religious prohibition should not be done unless the benefit of committing it outweighs its harm. Exceptions to this include necessities and needs, such as a husband and wife looking at each other, witnesses looking to bear testimony, doctors looking for medical treatment, looking at a prospective fiancée, establishing religious rituals like circumcision, removing harmful growths, and treating debilitating wounds. Looking at private parts requires an extreme need, which is even greater for women's private parts due to the fear of temptation.