Someone wiped over his shoes after wearing them in a state of purity, then took them off and prayed without them?
Ablution is not invalidated by taking off leather socks or shoes after wiping over them. However, whoever takes them off after wiping must wash his feet only. If he prayed without washing his feet, he must wash his feet and repeat the prayer. And Allah the Almighty knows best.
Is it permissible for a wife to boycott (not to attend to his different needs) her husband?
It isn`t permissible for the woman to boycott her husband unless he is the reason behind that, and it is recommended that both spouses seek the advice of righteous people to make reconciliation.
What is the ruling on a woman using contraception without her husband's knowledge if he is mistreating her?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
It is not permissible for a woman to use any means of delaying pregnancy without her husband's knowledge, consent, and mutual agreement. This is because having children is a sharʿī right belonging to both spouses equally in Islamic law. Imām al-Māwardī, may Allah have mercy upon him, stated: "The right to a child from a free woman is shared between them both" — meaning between the two spouses. [al-Ḥāwī al-Kabīr, 9/320]
It is therefore not permissible for either spouse to make a unilateral decision regarding the prevention of pregnancy without the consent of the other. We advise both spouses to discuss the matter with wisdom and mutual respect, so as to resolve any disagreement and arrive at a suitable solution that serves the interests of them both. And Allah the Almighty knows best.
When is it Sunnah to slaughter the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah for the 'aqīqah to be slaughtered on the seventh day from the birth of the newborn. According to the sounder position, the day of birth itself is counted as the first of the seven days. Thus, for example, if the child is born on a Saturday, the 'aqīqah is to be slaughtered on the following Friday. If the child is born at night, the count begins from the day that follows. And Allah Almighty knows best.