Is a wife considered divorced if her husband refused to go to bed with her (for sexual intercourse) for two months?
A wife doesn`t get divorced no matter for how long her husband refuses to have sex with her, and she had better go to court.
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 allowed for a Muslim woman to wear nail polish?
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.
Nail polish is an adornment that a woman is allowed to wear for her husband, and not in the presence of non-Mahram men. However, during ablution water needs to reach the nails, so it isn`t possible to perform 'Wudu (ablution) with nail polish on. Therefore, it isn`t valid to make Ghusl Jnabah (Ghusl performed after sexual intercourse or ejaculation), Ghusl after menstruation and Ghusl after Nifas (blood of childbirth) while wearing nail polish. And Allah The Almighty 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.