Is it permissible for a guardian (Big brother) to unlawfully stop his sister from getting married?
If the guardian denies her right in getting married for an unlawful reason, she should go to court in order to settle that matter, and the guardian is considered sinful in this case.
Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
Is the one offering the sacrifice liable if its meat spoils?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
If the meat (of the sacrifice) spoils due to the negligence of the one offering the sacrifice in preserving it, or due to improper storage, then he is liable to compensate for the portion due to the poor (which is estimated as half a kilogram of meat). If the sacrifice was a vowed (mandatory) one, then he is liable for all of it.
However, if he was not negligent, then there is no liability upon him, because its ruling is the ruling of a trust (like an item left in someone's care). And Allah Almighty knows best.
What is the best manner in distributing the meat of the Aqeeqah?
It is better to divide all of it as cooked meat amongst the poor and the needy. Dividing it into three portions is a Sunnah, but it is permissible to keep all of it provided that a portion, even a small one, is given to the poor and needy (one kilo for example).