Can a menstruating woman listen to the Quran from the radio or television?
Yes, a menstruating woman is allowed to listen to the Quran from the radio or television. What is forbidden for her is reciting the Quran and touching the Mus-haf, but listening is permissible—in fact, it is an act of worship.However, she should not repeat along with the Qur’an or try to keep pace with it.
Is it valid for the 'aqīqah to be performed using the newborn child's own wealth?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is not permissible for the guardian to perform the 'aqīqah using the newborn child's own wealth, because the 'aqīqah is a voluntary act of giving (tabarru'), and a guardian is prohibited from making voluntary expenditures from the child's wealth. Should he do so, he becomes financially liable for what he spent. And Allah Almighty knows best.
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.
Can Zakah or Zakat al-Fitr be given to a poor brother?
Yes, it is allowed to give Zakah or Zakat al-Fitr to a poor brother, as he is considered among the eligible recipients.