What is the ruling on wiping the front of the head beneath the ḥijāb, and is it permissible to wipe over the ḥijāb if it was put on while in a state of purification (wudu`)?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
It is permissible to wipe the front portion of the head (nāṣiyah) with the fingertips. It is likewise sufficient to place a wet hand over a head covering (ḥijāb), provided the moisture actually reaches the hair beneath it — if it does not, it does not suffice. A head covering is not treated in the same manner as leather socks (khuff) and may not be wiped over in lieu of the head itself.
Imām al-Nawawī, may Allah have mercy upon him, states in al-Majmūʿ (Vol.1/P.407): "If a person is wearing a turban and does not wish to remove it — whether for a valid reason or otherwise — he should wipe the entire front portion of the head... The same ruling applies to whatever a woman wears on her head. If, however, he confines himself to wiping over the turban without wiping any part of the head itself, this does not suffice — and there is no disagreement among us on this point." He further states: "A woman is like a man in the manner of wiping the head... She should insert her hand beneath her head covering so that the wiping falls upon the hair itself. If she places her wet hand over her head covering, our scholars stated: if the moisture does not reach the hair, it does not suffice her." And Allah the Almighty knows best.
What is the ruling on praying in congregation at the mosque?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Congregational prayer (Salat al-Jama‘ah) is a communal obligation (Fard Kifayah) for resident men regarding the performance of the prescribed (obligatory) prayers. For men, praying in congregation at the mosque is better than praying elsewhere, such as at home. On the authority of Abdullah bin Umar, the Messenger of Allah ﷺ said: 'Prayer in congregation is twenty-seven degrees more excellent than the prayer of a person alone' (Reported by Bukhari & Muslim). Furthermore, on the authority of Abu Hurayrah, the Messenger of Allah ﷺ said: 'Shall I not tell you that by which Allah erases sins and raises ranks?' They said, 'Of course, O Messenger of Allah.' He said: 'Performing wudu thoroughly despite difficulties, taking many steps toward the mosques, and waiting for the next prayer after the prayer; that is your Ribat (steadfastness)' (Narrated by Muslim).
As for a woman, her praying in congregation at home is better for her than in the mosque, according to the saying of our Master the Prophet ﷺ: 'Do not prevent your women from attending the mosques, but their homes are better for them' (Narrated by Abu Dawood). Young boys should be encouraged to attend the mosques and congregational prayers so they may become accustomed to them. And Allah the Exalted knows best.
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.
Is the one offering the sacrifice liable if its meat spoils?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
If the meat (of the sacrifice) spoils due to the negligence of the one offering the sacrifice in preserving it, or due to improper storage, then he is liable to compensate for the portion due to the poor (which is estimated as half a kilogram of meat). If the sacrifice was a vowed (mandatory) one, then he is liable for all of it.
However, if he was not negligent, then there is no liability upon him, because its ruling is the ruling of a trust (like an item left in someone's care). And Allah Almighty knows best.