Is it permissible for one to give the Zakah (obligatory charity) to his indebted brother?
It is permissible for one to give the Zakah to his brother if he was indebted, or poor.
Is it permissible for a woman to swear a false oath by the Holy Quran to please her distrustful husband?
It is forbidden for a person to do so since this is considered a false oath (Yamaan Ghamoos) which dips (Yaghmos) its taker in Hellfire if he/she doesn`t seek repentance, and he/she has to expiate for that oath. You should avoid any doubtful acts so that your husband`s chest remains clear from the evil suggestions of the devil.
I am a wholesale gold trader. My clients are retail gold shop owners. I sell them gold jewelry and ornaments on credit, and they repay me in weekly installments over a period of two months or more. The payments are made in cash for the labor charges and for the gold they owe me. In return, they may give me either cash or used gold.
It is not permissible to sell gold or silver on an installment basis or with a deferred payment; rather, immediate exchange is required. The Messenger of Allah (PBUH) 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 gives more or asks for more has engaged in usury; the giver and receiver are the same in this regard." (Muslim). Additionally, the weight of the gold must be equal when exchanging new for used; otherwise, it involves usury. The solution is to buy the used gold with cash, then sell the new gold for cash as well. However, payment must be made at the time of the transaction in both cases. Alternatively, one could take the used gold with the intention of refining it, reshape it into a new form, or repair it, then take a fee for the workmanship or repair. And Allah Knows Best
Does Husband fasting while being impure for having sexual intercourse with his wife at night permissible?
Yes it is permissible for you to fast because impurity isn't among valid fasting conditions, but you are obliged to perform ritual impurity in order to catch up Fajr prayer at its due time. And Allah Knows Best.