Is permissible to buy/sell with non-Muslim?
Yes buying/selling for a Muslim with non-Muslim is permissible as regards what is lawful.
Is it permissible for a Christian man to embrace Islam in secret and is it permissible for a Muslim woman to marry him?
Praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
His embracing Islam in secret is between him and Allah; however, it isn`t permissible for a Muslim woman to marry him except after he declares his Islam and it is ascertained that he is sincere about that. And Allah The Almighty Knows Best.
I`m a married young man. I fell in love with a widow and proposed to her but her family refused because they feared that this would have an adverse impact on the future of her children. However, we entered into unregistered marriage and told my family and even my wife about it. I`m a person who fears Allah, The Almighty and want to clear myself from any liability before Him, The Exalted. What should I do?
All perfect praise be to Allah the Lord of The Worlds. May His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
It is imperative that you proclaim this marriage to preserve rights. Therefore, you must register it in an Islamic court. A second marriage isn`t forbidden, however, if the unregistered marriage had taken place without the consent of the woman`s guardian nor the presence of two honorable witnesses, then it is considered void and your relationship with this woman is forbidden. Therefore, you must conclude a new marriage contract with the approval of her guardian and the presence of two honorable witnesses. We advise you to fear Allah and adhere to the teachings of Sharia in this regard since sinful conduct is that which turns in your heart (making you feel uncomfortable) and you dislike that it would be disclosed to other people. And Allah The Almighy 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.