Is it permissible to offer an Udhiyah on behalf of another without their permission?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is not permissible for a person to offer a sacrifice (Udhiyah) on behalf of someone else without their permission, except in the following cases: if he sacrifices on behalf of the members of his household, if a guardian sacrifices from his own wealth on behalf of his ward, or if the Imam (ruler) sacrifices from the public treasury (Bayt al-Mal) on behalf of the Muslims. And Allah the Almighty knows best.
Is it permissible for the guardian to give Sadaqa (voluntary charity) from the money of the orphans?
It is impermissible for the guardian to donate from the money of the orphans because he is entrusted with the safekeeping of that money, and is prohibited from donating it.
What is the ruling on swallowing phlegm while fasting?
If a fasting person intentionally swallows phlegm, their fast is invalid, as it is possible to avoid it.
However, if they swallow it unintentionally, their fast remains valid.
Phlegm is impure and should be avoided.
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.