What is the ruling on having brotherly ties between a strange man and a strange woman, and is the former considered a Mahram (unmarriageable) to the latter?
Such a relation between a strange man and a strange woman is forbidden in Islam because it involves forbidding what Allah has allowed by marriage, and allowing what Allah has forbidden such as looking and the like. Such a relation doesn`t render any act lawful between them, thus they are forbidden to look at each other, have a Khulwah (seclusion), and travel together.
What`s the ruling on using the following materials in manufacturing cosmetics: olive oil, Vaseline, talc powder, glycerin, honey, almond oil, pine oil, galingale and marjoram?
All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions. None of the above materials is forbidden, and it`s lawful to use them in manufacturing products that are beneficial to people. This is because, in principle, all things are lawful so long as there is no evidence in Sharia indicating otherwise. 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 Iddah period upon death of husband? What is the ruling when the woman observing Iddah after death of husband leaves her home to visit relatives although her Iddah hasn`t ended? What is the ruling on her wearing gold during Iddah period?
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.
For a woman whose husband has died, the 'Iddah* is four months and ten days after the death of her husband. If a woman is pregnant, the 'Iddah lasts until she gives birth. Moreover, she has to mourn, not wear gold, perfume nor saffron-colored garment. The evidence on this is that The Prophet (PBUH) said: "It is not lawful for a Muslim woman who believes in Allah and the Last Day to mourn for more than three days, except for her husband, for whom she should mourn for four months and ten days." [Agreed upon]. And Allah The Almighty Knows Best.
*The iddah is a waiting period that a Muslim woman observes after the death of her husband or after a divorce. The Quran says: For those men who die amongst you and leave behind wives, they (the wives) must confine themselves (spend iddah) for four months and ten days.