Should missed Sunnah prayer be made up?
Making up missed voluntary acts of worship is from Sunnah.
What are the conditions that must be met for the 'aqīqah to be valid?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The 'aqīqah is like the recommended uḍḥiyyah in terms of the type of animal, its age, and its required characteristics — since it is a recommended slaughter and therefore resembles the uḍḥiyyah in its rulings.
It is agreed upon without any difference of opinion that the 'aqīqah is not valid with any animal other than livestock (al-na'am — camels, cattle, and sheep). Likewise, an animal with a disqualifying defect — such as obvious illness, lameness, or blindness in one eye — does not suffice, as has previously been explained in the rulings of the uḍḥiyyah. And Allah Almighty knows best.
What is the ruling on offering the sacrifice (uḍḥiyah) using the wealth of a minor or a legally incompetent person (safīh)?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
It is not permissible for the guardian (walī) of an orphan or a legally incompetent person (safīh) to offer the sacrifice (uḍḥiyah) on behalf of the minor or the safīh using their wealth, because the guardian is charged with exercising caution over their wealth and is prohibited from giving any of it away voluntarily, and the udḥiyah is a voluntary act of charity (tabarru'). The guardian may, however, offer the sacrifice using his own personal wealth. And Allah, the Most High, knows best.
Is it permissible to give multiple mudds (portions) of fidyah to a single person?
Yes, it is permissible to give multiple mudd of fidyah to a single person, because each day of fasting is considered an independent act of worship.