Is the prayer of someone who didn`t face Quibla (Ka`ba direction) valid?
All perfect praise be to Allah,The Lord of The Worlds. Facing the Quibla is a condition for the validity of prayer, and the prayer of the person who hadn`t faced the direction of the Quibla is invalid, and he is obliged to repeat it. And Allah Knows Best.
Is it permissible to slaughter a single sheep with the combined intention of both the uḍḥiyyah and the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
According to Shaykh al-Islām Imam Ibn Ḥajar al-Haytamī, it is not permissible to combine the intention of the uḍḥiyyah and the 'aqīqah in a single animal, as each of the two has a distinct and separate cause that differs from the other.
However, Shaykh al-Islām Imam al-Ramlī permitted the combining of both intentions in a single animal — and this position offers a degree of latitude and ease. And Allah Almighty knows best.
Is it permissible for someone who is unable to fast to pay the fidyah (ransom/compensation payment) to himself, due to his own poverty?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
It is not permissible, nor does it fulfill the obligation, for a sick person who is currently and permanently unable to fast to pay the fidyah (ransom/compensation payment) to himself, since it is a financial obligation owed by him, established as a standing debt upon him — much like any other debt he owes. If he were to pay it to himself, it would not thereby be discharged. So if he cannot find [anyone eligible to] pay it to, it remains a standing obligation upon him, and is not thereby waived. If Allah, the Mighty and Majestic, later grants him wealth, it becomes obligatory upon him to pay it out to the poor and needy.
Imam al-Khaṭīb ash-Shirbīnī (raḥimahullāh) said: "There is no difference in the obligation of the fidyah between the wealthy and the poor person; its benefit lies in its remaining established as a standing debt upon the poor person [until he is able to pay it] — and this is the more correct position (al-aṣaḥḥ), as indicated by the wording of ar-Rawḍah and its source text." [Mughnī al-Muḥtāj, Vol.2/P.174]
Accordingly: it is not permissible for a Muslim to pay the fidyah to himself while he remains poor. If the sick person is poor, he is not obligated to pay the fidyah immediately, and it remains a standing debt upon him until a time when he has sufficient means and wealth. And Allah, the Exalted, knows best.
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.