Is it permissible for a wife to leave her house without obtaining the permission of her husband, and not to come back unless he divorces her co-wife?
It is forbidden for the wife to leave without obtaining her husband`s permission, and it is impermissible for her to ask him to divorce her co-wife as this inflicts harm on the latter and such an act is forbidden in Islamic law.
Is it permissible to make up for missed fast after the beginning of the second half of the month of Sha`ban (the month before Ramadan)?
Yes, it is permissible, but one who had missed fasts should hasten to make up for them. As for the Hadith mentioned in this regard, the prohibition is for offering absolute voluntary fasting. And Allah Knows Best.
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
Is it permissible for a person to sever ties with his sister because her husband had quit prayer and done him harm?
A sister is a blood-relative and maintaining blood-relations is obligatory in Islam. As regards her husband, he should be invited to the way of Allah with wisdom and beautiful preaching.