Is permissible to buy/sell with non-Muslim?
Yes buying/selling for a Muslim with non-Muslim is permissible as regards what is lawful.
What husband's stand should be, if his wife disagrees with his mother?
Both the mother and the wife have rights on you (Questioner); therefore, you are obliged to treat both justly, resort to wisdom to please both and intiate reestablishing cordial relations among them. And Allah Knows Best.
After a month and a half from the end of postpartum bleeding, my wife occasionally finds a small amount of blood, and she is breastfeeding. What is this blood, and should she fast and pray when she experiences it?
This is postpartum bleeding, so she should not fast or pray until she sees the signs of purity, unless it exceeds sixty days, as the maximum duration for postpartum bleeding is sixty days, and the majority of women experience forty days. If it exceeds sixty days, it is considered irregular bleeding (Istihada). It would be advisable to consult a doctor after the sixty days. And Allah Knows Best.
Is it permissible to watch soap operas during leisure time?
All perfect 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.
The answer depends on what is shown in them. If they include what is forbidden to see or hear then they aren`t permissible to watch. And Allah The Almighty Knows Best.