Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
Is it permissible to make up for missed fast after the beginning of the second half of the month of Sha`ban (the month before Ramadan)?
Yes, it is permissible, but one who had missed fasts should hasten to make up for them. As for the Hadith mentioned in this regard, the prohibition is for offering absolute voluntary fasting. And Allah Knows Best.
Is it permissible for a person to sever ties with his sister because her husband had quit prayer and done him harm?
A sister is a blood-relative and maintaining blood-relations is obligatory in Islam. As regards her husband, he should be invited to the way of Allah with wisdom and beautiful preaching.
Does passing wind from the anus affect ritual purity?
Ablution is nullified by the passing of wind from the anus, but washing the anus is not required as wind leaves no impurity.
