Is it obligatory to have an intention (niyyah) for every prayer?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is obligatory for the worshiper to have a specific intention (Niyyah) for every prayer, meaning they must consciously intend the act of worship they are performing. The intention is a pillar (Rukn) of the prayer, and the prayer is not valid without it. It is not a requirement to utter the intention verbally; rather, doing so is considered a recommended Sunnah. 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.
When does the time for the 'aqīqah lapse and pass?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
If the guardian was financially capable (mūsir) during the majority of the postnatal period (nifās) — which is sixty days — then the obligation of the 'aqīqah remains upon him until the child reaches the age of maturity (bulūgh). Once the child reaches maturity, the demand falls away from the father and those like him. At that point, it becomes Sunnah for the child himself to perform the 'aqīqah on his own behalf.
However, if the guardian was financially incapable (mu'sir) during the postnatal period, and then became financially capable after its expiry — that is, after sixty days — the 'aqīqah is no longer required of him. And Allah Almighty knows best.
What is the correct point at which to raise the hands when standing up for the third rak‘ah (after the middle tashahhud)?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Raising the hands while saying the takbīr [when rising for the third rak‘ah] is a recommended sunnah, and omitting it does not affect the validity of the prayer. The proper time for this is after rising from the middle tashahhud, once one has fully stood up.
It is stated in I‘ānat aṭ-Ṭālibīn (Vol.1/P.158): "His statement, 'and rising from the first tashahhud' — meaning, this manner [of raising the hands] is also a sunnah when he rises from the first tashahhud, that is, when he stands upright from it.
Consider [the question]: when precisely does the raising of the hands begin? Is it at the very start of rising from the first tashahhud, or after he has reached the minimum position of rukū‘ [i.e., once fully upright]? The apparent, [correct] view is the latter — even though the outward wording [of the text] might suggest the former — because at the very start of his rising, he is still relying on both hands [to push himself up, and therefore cannot yet raise them]."
It is stated in ‘Umdat as-Sālik (p. 53): "If his prayer extends beyond two rak‘ahs, he sits after them in the iftirāsh position, recites the tashahhud, and sends blessings upon the Prophet ﷺ alone, without [mentioning] his family [at this point]. He then stands while saying the takbīr, supporting himself with his hands; and once he has stood upright, he raises them level with his shoulders." And Allah, the Exalted, knows best.