Is supplicating in Qunoot, at times of affliction, during obligatory and voluntary prayer a Sunnah, and should it be done before Rukoo` (bowing), or after it?

At times of affliction, it is a Sunnah that Muslims supplicate in Qunoot after the final Rukoo` of each obligatory, or voluntary prayer as individuals, or in congregation.

Is it permissible for a pious Muslim woman to stay with her husband who had quit praying out of laziness?

Quitting prayer is one of the major grave sins that come after disbelieving in Allah, but the wife of such a person isn`t considered divorced, rather, she should exert all her efforts in order to bring him back to the way of Islam. However, if his sin is likely to lure her from the way of Islam, then she had better separate from him by lawful means such as Mokhal`aa (When a wife pays a compensation for her husband in return for divorcing her). Moreover, if she exercises patience, and remains steadfast on her faith, then there is no harm in doing that.

Are school exams a valid excuse for breaking the fast in Ramadan?

School and university exams are not considered a valid excuse for breaking the fast, as most students take their exams while fasting without experiencing extreme hardship. Fasting does not conflict with exam preparation, and a Muslim seeks strength in obedience to Allah for both worldly and spiritual matters.

Is it permissible for the person who hasn`t made wudu` (state of minor ritual impurity) to perform the Adhan?