Is it permissible to offer mandatory prayer while sitting?
All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions. Standing up is a pillar in the mandatory prayer and the prayer is not valid without it unless one cannot do it. As for Nafila (supererogatory prayer), one can perform it in the state of sitting even if he/she can stand, but his/her reward is half the reward of the person who prays while standing if he/sh has no legal excuse for such an act. And Allah Knows Best.
Is the son of the sister by breastfeeding considered a mahram in Islam, and is it permissible for a woman to go for Hajj with him?
Everything that is prohibited by lineage is also prohibited by breastfeeding. The son of the sister by breastfeeding is considered a mahram, just like the son of the sister by blood, and it is permissible for him to be her mahram for Hajj and Umrah. And Allah Knows Best.
What is the ruling on visiting a deceased's grave and supplicating Allah for him by his wife? Is the reward of reciting verses of the Holy Qur'an reaches the deceased?
There is no harm on visiting graveyard by woman with the intention of piety so long as they are dressed in accordance to the Islamic teachings. We ask Allah, The Almighty that the reward of reciting the Holy Qur'an on dedicated to the deceased reaches him. 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