What is the ruling on eating or drinking during the first Adhan?
It is permissible to eat and drink during the first Adhan because it takes place before the break of dawn. The purpose of this Adhan is to notify Muslims of the approaching dawn so they can prepare to stop eating when they hear the second Adhan.
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.
If someone delays making up fasts for a year, can they give fidyah before performing qada?
Yes, it is permissible to give fidyah before making up the missed fasts (qada), because each is an independent obligation, and there is no required order between them.
Is it permissible to purchase the Udhiyah on installments?
It is permissible to purchase the sacrificial animal (uḍḥiyyah) on installments or by borrowing its price. However, it is not recommended for the poor to do so, because they are not required to offer a sacrifice, and Allah does not burden a soul beyond its capacity. If doing so would lead to negligence in providing for one's dependents (nafaqah wājibah), then giving precedence to obligatory maintenance over borrowing to buy the sacrifice is appropriate. This is based on the saying of the Prophet (peace and blessings be upon him): "It is sufficient sin for a person to withhold food from those whom he is responsible to support."
Furthermore, the sacrifice is valid from one who has a debt, but it is preferable (awlā) to repay the debt first, especially if the debt is due immediately (ḥāll). And Allah Almighty knows best.