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 monetary value for the expiation of an oath (Kaffarat al-Yamin)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The expiation for an oath (Kaffarat al-Yamin) consists of feeding ten (10) needy persons. This is estimated at 600 grams of rice per person. It is also permissible to pay its value in cash, which is estimated at one dinar (per person). And Allah the Exalted knows best.
What is the ruling of Islamic Law on someone who wakes up in a state of janābah (major ritual impurity) near the very end of the prayer's designated time, during cold weather — should he heat water in order to perform ghusl, even though the prayer's time will expire as a result, or should he perform tayammum instead?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
If the water is cold, and cannot be used due to fear of harm that is not ordinarily tolerable, or that would result in illness, then in this case it becomes obligatory to heat the water — even if heating it causes the time for Fajr to expire — and no sin is incurred in doing so, due to his valid excuse. He may not resort to tayammum (dry ablution) instead, since water remains available [and merely needs to be heated].
Imam Shihāb ad-Dīn Aḥmad ar-Ramlī (raḥimahullāh) said: "He was asked regarding a person who, if he were to use cold water, would experience harm that permits tayammum, and who has access to something with which he could heat the water — but if he heats it, the prayer's time will expire. Is it obligatory for him to heat it even if the time expires, or should he pray with tayammum within the prescribed time? He answered that it is obligatory for him to heat the water, even if the time for that particular obligatory prayer expires." [Fatāwā ar-Ramlī, Vol.1/P.98]
Imam al-Bājūrī (raḥimahullāh) said in his Ḥāshiyah on Sharḥ Ibn Qāsim (Vol.1/P.173): "And if he fears [harm] from using cold water, and is currently unable to heat it, but knows of a place where firewood is available, such that if he were to go there he would not return until after the prescribed time has expired — what appears [to be the correct position] is that it is obligatory for him to go and seek the firewood, even if the time expires as a result, as this is the position ultimately settled upon by ar-Ramlī, and as related from him by Ibn Qāsim." And Allah, the Exalted, knows best.
What should the one performing the slaughter say at the time of slaughtering the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah to say the following supplication at the time of slaughtering the 'aqīqah:
"Bismillāhi wallāhu Akbar, Allāhumma laka wa ilayka, hādhihi 'aqīqatu fulān."
("In the name of Allah, and Allah is the Greatest. O Allah, this is for You and unto You — this is the 'aqīqah of [the child's name].")
This is based on what al-Bayhaqī narrated in Al-Sunan al-Kubrā (Vol.9/P.511), that the Prophet ﷺ said: "Slaughter it in his name and say: In the name of Allah, and Allah is the Greatest. O Allah, this is for You and unto You — this is the 'aqīqah of so-and-so."
And Allah Almighty knows best.