What is the ruling on a person in a state of major impurity (junub) or a menstruating woman (ha'id) reciting the Quran from memory?
It is not permissible for a menstruating woman, a postpartum woman, or a person in a state of major impurity to recite anything from the Quran, whether from memory, from the Quran, from a phone, or a computer. It is also not permissible for them to touch the Quran, based on what was reported from Ali bin Abi Talib that the Prophet (peace be upon him) was not prevented from anything regarding the Quran except major impurity (janabah). (Reported by al-Tirmidhi who said it is a hasan sahih hadith). Menstruation and postpartum bleeding are analogous to major impurity (janabah) as they are all major impurities (hadath akbar).
For those mentioned, it is permissible to mention Allah and supplicate even with verses from the Quran, provided they do not intend them as recitation of the Quran, but intend them as remembrance (dhikr) or supplication (du'a). And Allah the Almighty knows best.
What is the ruling of Islamic Law on selling gold or silver in installments or for a differed price?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is prohibited (haram) to sell gold or silver in installments or for a deferred price; rather, immediate hand-to-hand exchange (Taqabud) is mandatory, otherwise, it is considered usury (Riba). The Messenger of Allah ﷺ said: 'Gold for gold, silver for silver, wheat for wheat, barley for barley, dates for dates, and salt for salt—like for like, hand to hand. Whoever increases or asks for an increase has engaged in Riba; the receiver and the giver are the same in this regard.' (Narrated by Muslim). Furthermore, when exchanging new gold for used gold, they must be of equal weight, or it falls into Riba.
The permissible solution (al-makhraj) is for the merchant to purchase the used gold for cash first, and then sell the new gold for cash in a separate transaction. However, the price must be paid during the sitting of the contract (Majlis al-Aqd) for both deals. Alternatively, the jeweler may take the used gold with the intent of remodeling or repairing it, and then charge a fee for the craftsmanship or repair work. And Allah the Exalted knows best."
What is the ruling on water present on the floor of a toilet/bathroom?
The default ruling is the purity of this water present on the bathroom floor. If one is certain or strongly suspects its impurity, then one washes whatever part of the body or clothing this impure water has touched. If one doubts its impurity, the default is purity, and we do not rule it impure based on mere doubt. And Allah the Almighty knows best.
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.