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 it a condition that a woman should untie her locks while making Ghusl (ritual bath)?
Ghusl from Janabah (ritual impurity), or menstruation obligates that water reaches the roots of the hair in order for the Ghusl to be valid, but if it doesn`t, then hair locks must be untied for water to reach them, and for Ghusl to become valid.
What is the ruling of Islamic Law on a fictitious marriage for the purpose of obtaining citizenship?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
There is no such thing in our noble sharīʿah as a "nominal" or "fictitious" marriage or divorce. Marriage and divorce are among the sacred ordinances of Allah, and it is not permissible to manipulate them or use them as a stratagem to obtain worldly gains.
The foundational purpose of a marriage contract is the permanence and continuity of the relationship between the spouses — to establish a family, and to bring forth righteous offspring. So sacred is this bond that Allah the Almighty Himself described it as a solemn covenant (mīthāq ghalīẓ), saying {what means}: "And if you wish to replace one wife with another and you have given one of them a great amount of wealth, do not take any of it back. Would you take it in injustice and manifest sin? And how could you take it while you have gone in unto each other and they have taken from you a solemn covenant?" [Al-Nisāʾ/ 20–21]
Accordingly, it is not permissible to resort to manipulation and deception in contracts that Allah, Mighty and Majestic, has described as a "solemn covenant" — all for the sake of material and worldly benefit. Marriage is built upon permanence and does not admit of a fixed time limit. If a time limit is stipulated in the contract, the contract is rendered invalid by the consensus of the jurists. Similarly, marriage is impermissible when there exists a mutual, concealed intention to limit its duration — even if no time limit is explicitly mentioned in the contract — for this constitutes a form of unlawful circumvention of the sharīʿah. This is to say nothing of the lying and deception that such conduct involves, the prohibition of which needs no elaboration. Lying, deception, and fraud for the purpose of obtaining worldly gains are among the gravest of sins.
If, however, the marriage contract is first concluded in a valid sharʿī manner and then registered civilly, it is sound and fully valid. And Allah the Almighty knows best.
What is the ruling on using a miswak (tooth-stick) during the day in Ramadan?
It is permissible to use a miswak before noon while fasting. However, according to the Shafi'i school, it is disliked (makruh) after noon in order to preserve the natural effect of fasting in the mouth, as the Prophetﷺ said in authentic hadith:
"The breath of a fasting person is more pleasant to Allah than the fragrance of musk."