What is the ruling on congregational prayer performed outside the mosque, and is it a condition that it be performed in a mosque in order to attain the full reward?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
It is not a condition for attaining the reward of congregational prayer that it be performed in a mosque; however, a Muslim should still be keen to perform his prayers in the mosque, so as not to miss out on immense reward. This is due to the virtue of the mosque and of spending time there (i‘tikāf), the typically larger number of worshippers present, and the additional reward gained through walking to and from the mosque. On the authority of Abū Hurayrah (raḍiyallāhu ‘anh), the Messenger of Allah ﷺ said: "Whoever purifies himself in his house, then walks to one of the houses of Allah to fulfill one of the obligations Allah has prescribed, one of his steps will erase a sin, and the other will raise him a degree [in status]." (Related by Muslim)
Whoever misses congregational prayer at the mosque should still strive to pray in congregation at his workplace, or together with the members of his household. And Allah, the Exalted, knows best.
How should a person who is afflicted with continued major ritual impurity (incontinence of urine, bleeding outside the monthly period) perform ablution?
Such a person should make ablution for every prayer after its due time and after removing impurities from their body and outfit, and should place a fresh diaper whenever needed so as for the impurity not to spread out. They should also perform prayer immediately even if incontinence of urine continued, and should repeat the aforementioned for every obligatory prayer, then perform optional prayer as much as they want.
What should one who doubts the validity of his ablution and performs it frequently do?
Whoever doubts the validity of his ablution after finishing it, his ablution is valid. This is because the default is the validity of the ablution, and because doubt after finishing an act of worship doesn`t affect its validity. And Allah the Almighty 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.