Is it permissible for a woman to uncover her face while performing Umrah (minor Hajj)?
The woman while in a state of Ihram (ritual consecration) is obligated to uncover her face and hands, but at the same time permitted to let her head-covering garment drape from her head down over her face when non-Mahram (i.e., marriageable) men pass by her. And Allah Knows Best.
What is the ruling on entering the toilet with something containing the remembrance of Allah?
It is disliked to bring into the toilet anything containing a reminder of Allah, such as the Quran or a sacred name (like the name of Allah, Muhammad, etc.). If one does that, etiquette dictates that he conceal it so it is not visible while entering the toilet, either by cupping his hands over it, putting it in his pocket, or inside his shirt if it is a necklace or ring. And Allah the Almighty knows best.
Is it valid to perform the obligatory prayer while sitting?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Standing (Al-Qiyam) while having the ability to do so is one of the pillars (Arkan) of the prayer; the obligatory (Faridah) prayer is not valid without it. However, whoever is unable to stand may pray sitting down. As for voluntary (Nafilah) prayers, it is permissible to pray them sitting even if one is able to stand, but the one sitting receives half the reward of the one who prays standing. And Allah the Exalted 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.