Is it permissible to slaughter one animal as a sacrifice and an Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth)?
It is impermissible to do so since each of them is slaughtered for a different reason.
Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
What is the ruling on swearing on the Holy Quran and breaking that oath?
It is impermissible to swear on the Holy Quran in vain, and it is also impermissible to subject it to such an act since breaking the oath after swearing on the Quran entails an expiation.
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.