Should nail polish be removed before making ablution?
Yes, it should be removed because it prevents water from reaching the nails.
Is it permissible for a menstruating woman to recite the Quran from the computer without actually touching the Quran?
It is not permissible for a woman in her menstrual period, or in postpartum to recite the Quran, even by heart, or without actually touching the Quran itself. Recitation itself is what is prohibited on her regardless of how it is done. However, it is permissible for her to surf through the Quran by her eyes, or to recall it in her head without uttering the words. There is no harm for her to look at the Quranic verses on the computer without touching it, or to utter the words as this is called looking not reciting or reading.
What is the ruling on a mother giving the Zakat of her wealth to her children?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is permissible for a mother to give her children from the Zakat if they are among those who are eligible for it—such as being poor (Fuqara), possessing no wealth, and not being sufficiently provided for by the maintenance (Nafaqah) of others. This is based on the statement of the Messenger of Allah ﷺ regarding Zaynab, the wife of 'Abdullah ibn Mas'ud (may Allah be pleased with them both): (Your husband and your children are the most deserving of those upon whom you spend in charity) [Narrated by Al-Bukhari].
It is stated in [Al-Hawi al-Kabir, Vol. 8/P.537]: 'As for the wife, it is permissible for her to pay her Zakat to her husband from all the designated shares... Our evidence is the generality of the saying of Allah the Almighty: "Zakat expenditures are only for the poor and for the needy", and the Hadith of Abu Hurairah that the Prophet ﷺ said to Zaynab, the wife of 'Abdullah ibn Mas'ud: (Your husband and your children are the most deserving of those upon whom you spend), and this is taken in its general sense.' And Allah the Exalted knows best.
Is it permissible to sleep before the time of the Fajr prayer begins, with the intention of waking up shortly afterward?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible for a Muslim to sleep before the time of the Fajr prayer begins, intending to wake up and perform the prayer, by setting an alarm or asking someone to wake him. What is to be avoided is that a person sleeps while he predominantly assumes that he will not wake up for the prayer.
If he does not wake up until the time of the prayer has ended, he must make it up. It is recommended that he hasten to make it up as soon as he wakes, and likewise recommended that he make up its sunnah along with it.
It is stated in al-Majmūʿ by Shaykh al-Islām Imam al-Nawawī (may Allah have mercy on him): “Whoever was obliged to pray and did not pray until the time passed must make it up, because of the saying of the Prophet (peace and blessings be upon him): ‘Whoever sleeps through a prayer or forgets it, let him pray it when he remembers it.’ It is recommended that he make it up immediately, because of the ḥadīth we have mentioned. If he delays it, that is permissible, because it is reported that the Prophet (peace and blessings be upon him) missed the Fajr prayer and did not pray it until he had left the valley. Had it been required immediately, he would not have delayed it. Abū Is-ḥāq said: If he left it without a valid Sharia excuse, he must make it up immediately, because he was negligent in delaying it.”
It is therefore the duty of every Muslim to keep the prayer in its proper time, seeking help from Allah the Exalted and striving against the self to do so. And Allah Almighty knows best.