Is it permissible for me to make up for my late father`s missed fasts? and should I make an intention to this end by saying: "I intend to make up for my late father`s missed fasts?
It is permissible to fast on behalf of the deceased father in order to make up for his missed fasts, and you should make the intention for offering fast from night time, but uttering the intention isn`t a condition. And Allah Knows Best.
Is it permissible to single out Fridays, Saturdays, and Sundays to make up for missed fasting without fasting a day before ,or after each ?
Yes, it is permissible to make up for missed fasting during the aforesaid days, and it is also valid to offer non-obligatory and vowed fasting as well. However, fasting a day before or after each isn`t obligatory. And Allah Knows Best.
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 is the stance of Ahlus-Sunnah wal-Jama'ah regarding the historical figure known as 'the Sufyani,' who some say will appear at the end of times? And what is the stance of Ahlus-Sunnah wal-Jama'ah regarding the group that killed Al-Husayn ibn Ali (may Allah be pleased with them), particularly those who directly committed the killing, severed his head, and killed members of his family?
Most of the narrations about the signs of the Hour concerning the Sufyani, who is said to appear before the Mahdi, indicate that he is the leader of the army that will invade the Kaaba, and Allah will cause the earth to swallow them. We disassociate ourselves before Allah from those who killed Al-Husayn Ibn Ali (may Allah be pleased with them), supported his killing, or encouraged it, whether openly or secretly. The inner matters are left to Allah alone. And Allah The Almighty Knows Best.