Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
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."
Does the fast become invalid if water from rinsing the mouth reaches the stomach while performing ablution?
If water reaches the stomach without the fasting person exceeding normal rinsing or being excessive, their fast remains valid.
However, if they exceed the normal practice or exaggerate in rinsing, causing water to enter the stomach, their fast is invalid.
This is because excessiveness in rinsing is prohibited for a fasting person, as the Prophetﷺ said: "Exaggerate inhaling water during ablution, except when you are fasting." [Narrated by the Four Imams]
Transgression (Ta‘addi) refers to rinsing the mouth more than three times, while exaggeration (Mubalaghah) includes gargling, drawing water deep into the nasal passages, or filling the mouth with water in an unusual manner.
How is the niṣāb (minimum threshold) of gold calculated when one owns gold of multiple different karats?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Zakāh is obligatory on cash and on gold designated for saving or for trade, provided the total reaches the niṣāb (minimum threshold liable for Zakah), and a full ḥawl (lunar year) has elapsed over it. The niṣāb is (85) grams of 24-karat gold; for 21-karat gold, the niṣāb equals (97) grams; and for 18-karat gold, it equals (113) grams.
If one owns gold of multiple different karats, the person paying zakāh should calculate the monetary value of all the gold he owns, combining these values together to determine whether the total reaches the niṣāb. He then pays zakāh on this combined monetary value, once the total reaches the niṣāb. The relied-upon position is to calculate the zakāh based on the buying price [i.e., the price the gold merchant would pay the owner to purchase the gold from him] on the day the zakāh obligation is due. And Allah, the Exalted, knows best.