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.
Is a woman sinful if she fasts out of shyness from her family while menstruating or in postnatal bleeding?
It is forbidden for a woman who is menstruating or in postnatal bleeding to abstain from food and drink with the intention of fasting. If she fasts out of shyness, she is sinful, as her fast is not valid.
However, if she refrains from eating and drinking without intending to fast, it is not forbidden, but she unnecessarily burdens herself without need.
What is the ruling on discharging one's zakāh obligation through the provision of a specific benefit (manfa‘ah) — such as performing a surgical operation for a patient, or providing housing to a tenant, and counting the value of this service as zakāh?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
It is obligatory to pay zakāh from the actual asset (‘ayn al-māl) upon which zakāh is due, except in the case of zakāh on trade goods ('urūḍ at-tijārah), which is paid based on their monetary value. In all cases, zakāh must be given in the form of tamlīk (a full transfer of ownership), based on the words of Allah, the Mighty and Majestic (which mean): "Zakāh expenditures are only for the poor and for the needy, and for those employed to collect [zakāh], and for bringing hearts together [for Islam], and for freeing captives [or slaves], and for those in debt, and for the cause of Allah, and for the [stranded] traveler — an obligation [imposed] by Allah. And Allah is Knowing and Wise" [at-Tawbah/60]. The letter "lām" (لِ) in this verse — as in "lil-fuqarā'" ("for the poor") — indicates possession/ownership (lām al-milk).
It is not permissible to fulfill one's zakāh obligation by providing a benefit or service (manfa‘ah) — such as housing, education, or medical treatment — in place of the zakāh itself. This is because zakāh must be paid as wealth (māl) that is transferred into the ownership of the poor recipient, whereas such services are intangible benefits that are not, in themselves, capable of being formally transferred in ownership (ghayr qābilah lit-tamlīk). And Allah, the Exalted, knows best.
Which takes precedence: the 'aqīqah or the uḍḥiyyah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The 'aqīqah is an act of worship through which a servant draws closer to Allah the Almighty in gratitude for the blessing of a newborn child. It is a confirmed Sunnah for those who are financially capable, and Allah does not burden any soul beyond what it can bear.
However, the uḍḥiyyah takes precedence, as it is a confirmed Sunnah established from the Prophet ﷺ through stronger and more numerous narrations — indeed, the Ḥanafī scholars hold it to be obligatory. Furthermore, its time is narrow and limited, expiring with the passing of the days of Eid, whereas the 'aqīqah may be delayed until one becomes financially capable of performing it.
And Allah Almighty knows best.