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.
Is it permissible to go to the bathroom wearing a necklace that has the word "Allah" inscribed on it?
All Perfect Praie be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.
Anything that contains words pertaining to Allah, The Almighty, is desired to be left outside when going to the bathroom, or to be hidden for fear of losing it. And Allah Knows Best.
Is Iddah (waiting period) incumbent on an old lady whose husband had died?
Upon the death of the husband, Iddah is incumbent on the wife regardless of her age.
My husband told me that he concluded our marriage with a fake name that belongs to another person, because he was sentenced. Nowadays, he brought an ID, passport and birth certificate with the his current name. What is the ruling on being married to him?
praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
As regards being married to the person mentioned in your question: The marriage is valid so long as he was the same person your guardian concluded the marriage with, even if he changed his name i.e. if your marriage contract was concluded with the same person, since what counts regarding marriage is the persons not names. And Allah Knows Best.