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.
Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
Is it permissible for a woman to offer the obligatory prayer after Adhaan (call for prayer), and before Iqamah (The announcement that the prayer is about to begin) in the mosque?
Yes, it is permissible for a woman to offer the obligatory prayer immediately after the Adhan and before the Iqamah in the mosque. And Allah Knows Best.
What is the ruling on performing istinja' with perfumed tissues or a tissue moistened with water?
Performing istinja' with perfumed or moistened tissues is not sufficient if they are not dry, due to the moisture on them reaching the impurity, which increases its spread rather than reducing it. Then, to remove the impurity, one must use pure water. And Allah the Almighty knows best.