Is it a condition for the mosque where I‘tikaf is performed to hold Jumu‘ah prayers?
No, it is not a condition for the mosque where I‘tikaf is performed to have Jumu‘ah prayers. However, if a person vows to perform continuous I‘tikaf, and Jumu‘ah occurs within that period, then they must observe I‘tikaf in a mosque where Jumu‘ah is held so that they do not break their continuity by leaving for Friday prayer.
Is it recommended (mustaḥabb) for the one offering a voluntary sacrifice (uḍḥiyyat taṭawwuʿ) to eat from its meat?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
It is recommended (mustaḥabb) — not obligatory — for the one offering a voluntary sacrifice (uḍḥiyyat taṭawwuʿ) to eat from it. Allah Almighty says {what means}: "So eat from them and feed the desperate (qāniʿ) and the beggar (muʿtarr). Thus We have subjected them to you that you may be grateful."— [Sūrat al-Ḥajj (22): 36]
Explanation of terms:
Al-Qāniʿ — the poor person who does not ask people for money, food..eccetera.(beg)
Al-Muʿtarr — the poor person who does ask people for money, food..eccetera (begs)
And Allah Almighty knows best.
Is it permissible for one who sacrifices on behalf of another, with the latter's permission, to eat from the sacrifice?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is permissible for one who sacrifices on behalf of another with his permission to eat from the sacrifice with his permission, and he takes his place in distributing its meat.
It is stated in Hashiyat al-Jamal 'ala Sharh al-Minhaj (Vol.5/P.262): 'If a person sacrifices on behalf of a living individual with his permission, does he take the place of that individual in distributing the meat, because permission for the sacrifice implies permission for distribution, or does it depend on explicit permission? There is room for consideration, but the former view is not far-fetched.' And Allah Almighty knows best."
What is the ruling on performing dry ablution (tayammum) instead of the ritual bath due to severe cold?
Whoever is sick such that he cannot use water, or finds the water cold and heating it is not possible, and the person would be harmed by using cold water, it is permissible for him to perform tayammum. He must make up what he prayed with tayammum, because this is a place where there is water. And Allah the Almighty knows best.