Is it permissible to make ablution without answering the call of nature after waking up?
Washing front and back openings (Istinjaa`) is not a condition for the validity of ablution because it is done to remove Najaasah (impurity), thus if there is no Najaasah, there is no need for that, and then it is permissible to make ablution without answering the call of nature. However, prayer is invalidated if there is Najaasah on the anus ,or the front opening, so it (Najaasah) must be removed for the prayer to become valid, and not the ablution.
Is the father a Mahram (Non-marriageable) to his son`s mother-in-law?
The father is a non-Mahram (Marriageable) to his son`s mother-in-law, so it is impermissible for them to look at each other, or to have a seclusion (Khalwah).
Is the Saying "Whatever is Taken by the Sword of Shyness is Forbidden" an Authentic Ḥadīth?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
The saying "Whatever is taken by the sword of shyness is forbidden" is not an authentic ḥadīth, though its underlying meaning is sound. The established sharʿī principle is that a Muslim's wealth is not lawful for anyone to take except with his wholehearted consent, as Allah the Almighty says {what means}: "O you who have believed, do not consume one another's wealth unjustly, but only [in lawful] business by mutual consent." [Al-Nisā/ 29] And the Messenger of Allah ﷺ said: "Listen to me and you will live well: do not wrong others, do not wrong others, do not wrong others. Indeed, a man's wealth is not lawful except with his full, willing consent." (Reported by Aḥmad in his Musnad.) Whatever is taken through the pressure of shyness or social embarrassment runs directly counter to genuine, wholehearted consent.
The jurists have explicitly stated that whatever is taken by means of the "sword of shyness" carries the same ruling as that which is taken by coercion — it must be returned to its rightful owner.
Ibn Ḥajar al-Haytamī, may Allah have mercy upon him, states in al-Fatāwā al-Kubrā (Vol.3/P.30): "Do you not see the reported scholarly consensus that whoever has something taken from him purely out of shyness, without his genuine consent, does not pass ownership of it to the one who took it? They reasoned that this constitutes a form of coercion through the 'sword of shyness,' comparable to coercion at the point of an actual sword. Indeed, many people would rather submit to the literal sword and endure the pain of its wound than submit to this first kind of coercion, out of fear for their dignity and standing — which people of sound judgment hold dear and guard most fiercely." And Allah the Almighty knows best.
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.
