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 the prayer of the individual following the imam whose prayer is broadcasted via television?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Among the conditions for the validity of following an Imam (Sihhat al-Iqtida’) is that the Imam and the follower (Ma’mum) must be in the same location. Therefore, the prayer of one who follows an Imam whose prayer is being broadcast via television from a distant location is not valid. However, if the follower is with the Imam in the same mosque, the prayer is valid. And Allah the Exalted knows best.
Does collecting saliva and swallowing it break the fast?
Swallowing collected saliva does not break the fast, but it is an unnecessary and meaningless act.
Is it permissible to slaughter sacrificial animals in public squares and streets?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The slaughtering of sacrificial animals (udhiyah) should take place in locations designated for slaughter, such as abattoirs (slaughterhouses), or in sites allocated by the relevant authorities for this purpose.
It is not permissible to perform slaughtering in a random or haphazard manner—such as in public squares, on roadsides, or in front of houses—in a way that creates health hazards, causes public nuisance, or endangers public safety. And Allah Almighty knows best.