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.
What is the ruling on making up the regular *rawātib* (sunnah) prayers together with a missed obligatory prayer?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is obligatory to make up (qaḍāʾ) a missed obligatory prayer (farḍ). As for the timed supererogatory prayers (al-sunan al-muʾaqqatah) or the regular rawātib prayers, it is recommended (mandūb) to make them up, even if a long time has passed. Ibn Ḥajar (may Allah have mercy on him) said in his Fatāwā: "It is established in our school that it is sunnah to make up the timed voluntary prayers, by night or by day, even if congregation is not prescribed for them, whether much time has passed or little."
Accordingly, it is recommended to make up the sunan together with the obligatory prayer. And Allah Almighty knows best.
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Note on terminology: Al-nawāfil al-muʾaqqatah (timed voluntary prayers) refers to supererogatory prayers tied to a specific time or cause, such as the rawātib (regular prayers before and after the obligatory ones), Duha, and the like. The ruling given here reflects the Shāfiʿī position.
What is the ruling on vomiting, and does it invalidate ablution?
Vomit is impure (najis). Its exit is not considered one of the nullifiers of ablution. However, the mouth must be washed and purified from it, and any that gets on clothing or the body must be washed for prayer, because prayer is not valid with impurity present on the body or clothing. And Allah the Almighty knows best.
Does using a respiratory device (oxygen) affect the validity of fasting?
Using an oxygen device does not affect the validity of fasting because oxygen is a gas with no physical substance.
However, if medicinal substances with physical particles are added to the oxygen, its use would break the fast, as it enters the body cavity through a natural passage.