When does the time for the Fajr prayer begin?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
The time for the Fajr prayer begins once the Mu’adhin starts the second Adhan (Al-Adhan al-Thani), and not after the first Adhan. And Allah the Exalted knows best.
What is the ruling of Islamic Law on making up missed voluntary prayers?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
It is recommended for a Muslim to make up any missed voluntary prayers — whether the regular Sunnah prayers (rawātib), the witr prayer, or his personal devotional routine (wird). As for voluntary prayers that are tied to a specific cause or occasion — such as the eclipse prayers (kusūf and khusūf) — these are not made up once their time has passed.
Shaykh al-Islām Imām al-Nawawī, may Allah have mercy upon him, stated: "The correct view in our school is that making up the regular voluntary prayers is recommended." [Al-Majmūʿ, Vol. 4/P.43] And Allah the Almighty knows best.
Does the intention (niyyah) of the principal (muwakkil) suffice for the sacrifice (dhabḥ) of the udhiyyah?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
If a person appoints an agent (wakīl) to perform the slaughter (dhabḥ) on their behalf, the intention (niyyah) of the principal (the one appointing the agent) suffices, and there is no need for the agent to have this intention himself. In fact, even if the agent is unaware that he is performing the sacrifice on someone's behalf as an udhiyyah (sacrificial offering), this does not affect its validity. And Allah, the Most High, knows best.
Is it valid to share in the 'aqīqah by contributing a seventh share of a camel or cow?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
Yes, it is permissible. If a group of people jointly share in the slaughter of a camel or a cow on behalf of seven individuals, this is valid — regardless of whether all of them intend the 'aqīqah, or some intend the 'aqīqah, others the uḍḥiyyah, and others simply the purchase of meat. And Allah Almighty knows best.