Is it valid for the 'aqīqah to be performed using the newborn child's own wealth?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is not permissible for the guardian to perform the 'aqīqah using the newborn child's own wealth, because the 'aqīqah is a voluntary act of giving (tabarru'), and a guardian is prohibited from making voluntary expenditures from the child's wealth. Should he do so, he becomes financially liable for what he spent. And Allah Almighty knows best.
What is the ruling on eating and drinking at night after making the intention? Is it necessary to renew the intention?
Eating and drinking at night, even after making the intention (for the next day), does not affect the fast, and it is not necessary to renew the intention after eating and drinking.
Is the niṣāb calculated based on the price of 21-karat gold, or 24-karat gold?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Zakāh is obligatory on cash and on gold designated for saving or for trade, provided the total reaches the niṣāb (minimum threshold liable for zakah), and a full ḥawl (lunar year) has elapsed over it. The niṣāb is (85) grams of 24-karat gold; for 21-karat gold, the niṣāb equals (97) grams; and for 18-karat gold, it equals (113) grams.
The relied-upon position is to calculate the zakāh based on the buying price [i.e., the price the gold merchant would pay the owner to purchase the gold from him] on the day the zakāh obligation is due.
The one paying zakāh may assess/calculate the niṣāb using any of the aforementioned gold karats [i.e., he may choose whichever karat standard he wishes for the purpose of the calculation]. And Allah, the Exalted, knows best.
What is the ruling on reciting aloud (*jahr*) in a silent (*sirriyyah*) prayer?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Reciting aloud (jahr) in the Fajr prayer, in the first two rakʿahs of Maghrib and ʿIshāʾ, and reciting silently (isrār) in the Dhuhr and ʿAṣr prayers is a sunnah. If the worshipper recites aloud where silence is prescribed, or the reverse, his prayer is valid, although it is better to follow the sunnah, in imitation of the Prophet (peace and blessings be upon him). Abū Hurayrah (may Allah be pleased with him) said: “In every prayer there is recitation. What the Messenger of Allah (peace and blessings be upon him) let us hear, we let you hear, and what he concealed from us, we conceal from you. If you add nothing to Umm al-Qurʾān (al-Fātiḥah), it suffices, and if you add to it, it is better.” Narrated by al-Bukhārī.
Shaykh al-Islām Imam al-Nawawī (may Allah have mercy on him) said in al-Majmūʿ (Vol.3/389): “The sunnah is to recite aloud in the two rakʿahs of Ṣubḥ (Fajr), Maghrib, and ʿIshāʾ, and in the Friday prayer, and to recite silently in Dhuhr, ʿAṣr, the third rakʿah of Maghrib, and the third and fourth of ʿIshāʾ. All of this is by the consensus of the Muslims, together with the mutually reinforcing authentic ḥadīths on the matter. This is the ruling for the imam. As for the individual worshipper (munfarid), it is sunnah for him to recite aloud according to us and according to the majority… If he recites aloud where silence is prescribed, or the reverse, his prayer is not invalidated, nor is there a prostration of forgetfulness (sujūd al-sahw) for it, but he has committed something disliked (makrūh).” And Allah Almighty knows best.