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.
What is the ruling on swallowing saliva while fasting?
It is permissible for a fasting person to swallow their saliva because avoiding it would cause undue hardship and excessive strictness in religion. Islam discourages such excessiveness since Allah the Almighty intends ease for His followers and does not intend to put them in hardship.
Is it permissible for a young man and a young woman to enter into a covenant as a married couple without having a true seclusion (Khalwah) until their marriage contract is officially concluded?
The relation which isn`t based on a marriage contract is forbidden, and entering into a covenant as a married couple is unaccounted for and is from the evil suggestions of the devil.
If someone starts the day sick or traveling while fasting, is it permissible for them to break their fast?
● A sick person who finds fasting difficult is allowed to break their fast, whether they began the day fasting or not.
● As for a traveler:
○ If they were still at home at dawn and then traveled after Fajr (dawn), they must continue fasting unless they experience extreme hardship, in which case they may break their fast.
○ However, if they were already traveling when dawn broke—meaning they had left their town before Fajr—then they are permitted to break their fast. This is what the Prophetﷺ did during the year of the conquest (of Makkah).