Is it permissible to divide one mudd of fidyah between two people?
No, it is not permissible to divide one mudd between two people, because it would not count as a full meal for either of them.
Is it permissible to use unscented petroleum jelly (Vaseline) during ‘Umrah, in order to prevent skin chafing or irritation?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
According to the Shāfi‘ī school, it is permissible for someone in the state of iḥrām to use oils and creams free of perfume/fragrance on parts of the body other than the head and beard, for a genuine medical need — such as preventing skin chafing or irritation. However, applying them to the head or beard remains unlawful.
Shaykh al-Islām, Imam an-Nawawī (raḥimahullāh), says in al-Majmū‘ (Vol.7/P.279): "Oils are of two types: the first is an oil that is neither perfumed itself nor contains any perfume — such as olive oil, sesame oil, ghee, butter, walnut oil, almond oil, and similar oils. The use of this type is not unlawful anywhere on the body, except on the head and beard — where its use is unlawful without any disagreement [among the scholars]." And Allah, the Exalted, knows best.
Who is responsible for performing the aqiqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The one upon whom the 'aqīqah is incumbent is whoever is obligated to financially maintain the newborn — whether the father, paternal grandfather, or mother. It is to be performed from their own wealth, not from the wealth of the newborn child.
As for one upon whom the financial maintenance of the newborn is not obligatory, they may not perform the 'aqīqah except with the permission of the one upon whom it is obligatory — namely, the father. And Allah Almighty knows best.
I have a date farm, and the dates come in different categories, and within each category there are different sizes. How is zakāh paid on the yield?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
If the yield reaches the niṣāb (the minimum threshold for zakāh to become obligatory) — which is five awsuq (plural of wasq), equivalent to (611) kg — then zakāh becomes obligatory upon it, at a rate of one-tenth ('ushr) if irrigated by rainwater (i.e., naturally, without the use of machinery), or one-twentieth (half of the 'ushr) if irrigated using machinery/equipment.
If the yield of dates consists of different varieties, then zakāh should be paid from each variety according to its respective proportion. If this proves difficult, it is permissible to pay from a medium-quality variety [representative of the average].
It is stated in Ḥāshiyatā Qulyūbī wa ‘Umayrah (Vol.2/P.22): "Different varieties are combined together [for the purpose of calculating the niṣāb] — such as the various types of dates, the various types of raisins, and so on — and zakāh is paid from each type according to its respective proportion. However, if this becomes difficult due to the large number of varieties and the small quantity of each individual type, then zakāh should be paid from a medium-quality variety among them — neither the best nor the worst — out of consideration for both sides [the giver and the poor recipient]. If one goes to the trouble of paying from each variety according to its proportion, this is also permissible." And Allah, the Exalted, knows best.