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 permissible for one who sacrifices on behalf of another, with the latter's permission, to eat from the sacrifice?
It is permissible for someone who sacrificed on behalf of another with their permission to eat from it with their permission, and they stand in their place (act as their representative) in distributing it.
It is stated in Nihayat al-Muhtaj ila Sharh al-Minhaj (Vol.8/P.141): "And he—meaning the one sacrificing on his own behalf, provided he has not apostatized—has the right to eat from a voluntary sacrifice and his sacrificial gift; rather, it is recommended. As for an obligatory sacrifice, it is forbidden for him to eat from it, whether it was designated as such initially or as a liability in his dhimmah. And excluded by what has preceded is if he sacrifices on behalf of another, or if he apostatized, then it is not permissible for him to eat from it, just as it is absolutely impermissible to feed a disbeliever from it."(The text I found indicates the impermissibility of eating) ???
And it is stated in Hashiyat al-Jamal ‘ala Sharh al-Manhaj (Vol.5/P.262): "If a person offers a sacrifice on behalf of a living person with their permission, does he act as their representative in distributing it—on the grounds that permission to sacrifice is permission to distribute it—or does it depend on their explicit permission? This requires consideration, but the first view is not far-fetched." And Allah the Almighty knows best.
Is Fajr (dawn) Sunnah a confirmed one?
All praise be to Allah The Lord of The Worlds Of course, it is a confirmed Sunna which the Prophet (PBUH) used to offer in a regular basis. And Allah Knows Best.
What is the ruling on someone who possesses cash reaching the niṣāb (minimum threshold liable for zakah), and then uses part of it to purchase gold before the ḥawl (lunar year) is complete — must he pay zakāh on all of it [combined], or only on the remaining cash, excluding the gold?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Gold acquired for hoarding and saving is subject to zakāh once it reaches the niṣāb (minimum threshold liable for Zakah) — when combined with any cash held — and once a full ḥawl (lunar year) has elapsed over it. The starting point for calculating this ḥawl is the ḥawl of the paper currency [used to purchase it], which had already reached the niṣāb and was then used to purchase the gold.
It is stated in Mughnī al-Muḥtāj (Vol.2/p.78): "As for someone who sells silver in exchange for gold, or vice versa, zakāh remains obligatory upon it, since he builds [the calculation of] its ḥawl upon [the ḥawl established at the time of] the original transaction [i.e., when the wealth was first acquired]."
This has already been explained in detail in Fatwa No.
2670 — please refer to it.
And Allah, the Exalted, knows best.
