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.
Is a woman`s prayer considered invalid if non-Mahrams (marriageable men) saw her offering it?
A woman`s prayer isn`t invalidated if non-Mahrams saw her offering it, but she had better pray in isolation.
What is the ruling of Islamic Law on Making up Prayers Missed before Reaching Puberty?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Among the conditions for accountability for one's actions in the Hereafter is taklīf (religious legal responsibility) — meaning, possessing sound reason and having reached puberty. The signs of puberty are: nocturnal emission, menstruation, or reaching the age of fifteen [lunar years].
Whoever missed prayers before reaching puberty is not obligated to make them up, since taklīf did not yet apply to him at that time. Our master, the Prophet ﷺ, said: "The pen has been lifted from three: from the child until he reaches puberty, from the sleeping person until he wakes, and from the insane person until he regains sanity." [Related by Abū Dāwūd]
The method for making up missed prayers and fasts has already been explained in Fatwa No.
2705, and Fatwa No.
876. And Allah, the Exalted, knows best.
Where should a woman following her husband or another man in prayer stand?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If a single woman prays with a man—whether she is his wife or a non-mahram (Ajnabiyyah)—the Sunnah is for her to stand behind the Imam and be shielded by him. If the Imam is leading both a man and a woman, the man should stand to the Imam's right, and the woman should stand behind the male follower (Muqtadi). In this way, she is shielded from the Imam by the male follower and remains at a distance from the follower and his line of sight. And Allah the Exalted knows best.