What is the ruling of Islamic Law on a person who abandons prayer after reaching puberty—is he required to make them up?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Making up missed obligatory prayers is an Islamic duty just as performing them in their proper time is obligatory, and taking care of them takes precedence over performing voluntary prayers. This is established by the practice of our Supreme Prophet (peace and blessings be upon him) when the polytheists distracted him on the Day of the Trench from performing the Asr prayer, so he made it up afterward, as well as the Hadith: "Pay Allah what is due to Him, for Allah is most deserving of fulfillment." (Recorded by Al-Bukhari)
Furthermore, it is valid to make up missed prayers at any time.
Whoever has missed a number of prayers and does not know their exact count, it is obligatory upon them to sincerely repent and exert their utmost effort to estimate their number. If they are unable to determine the exact count, they should base it on what is most probable according to their best judgment. They should then make them up gradually; if one performs one missed prayer alongside every current obligatory prayer, the matter becomes easy and manageable, and with the passage of time, one will complete what is owed, Allah willing. And Allah Almighty knows best.
I hired a private tutor for my son through an academy that sends teachers [to families] and takes a percentage [of their pay]. At the start of the [new] school year, I arranged directly with that same teacher, without the academy's knowledge. What is the ruling on this?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The ruling on this matter depends on knowing the specific terms of the agreement and contract concluded with the academy. If the agreement stipulates that no arrangement may be made with any of the students except through the academy itself, then it is not permissible for you to breach the terms of this contract, based on the words of our master, the Messenger of Allah ﷺ: "Muslims are bound by their conditions." (Related by al-Bukhārī)
However, if the agreement pertains only to teaching a specific subject, and the agreement concludes once that subject is finished, then there is no objection to arranging with the teacher to teach other subjects after the contract period has ended, outside of the academy.
Whatever the case maybe, the teacher must uphold the terms of his contract with the academy. And Allah, the Exalted, knows best.
Is it permissible for one to shake hands with his uncle`s daughter?
No, it isn`t because he is a non-Mahram (Marriageable) to her.
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.