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 wife to refuse to go to bed with her husband (for sexual intercourse)?
It isn`t permissible for her to do so unless for a sound reason.
Is it incumbent on a husband to pay the alimony of his wife if she had left him and stayed at her parent`s without his permission?
When a wife leaves her house, and stays at her parent`s without asking her husband, she is considered a Nashiz (wife who refuses to abide by her husband’s orders), and so she doesn`t deserve an alimony.
Is it permissible for a praying person to make supplication in each Sajdah (a prostration) of obligatory prayer?
It is permissible for a praying person, whether praying individually, or in congregation, to make supplication during Sujood (prostration) in obligatory, or voluntary prayers. However, it is disliked for the Imam to do so since he is required to spare the prayer performers any sort of hardship, unless he is leading a certain group who don`t mind him extending the prayer.