• 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?
All perfect 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.
• Is it permissible for a wife to refuse to go to bed with her husband (for sexual intercourse)?
It isn`t permissible for her to do so unless for a sound reason.
• What is the expiation for using perfumed soap while being in a state of Ihram(ritual consecration) for Umrah(after making the intent for Ihram)?
It is impermissible to use perfumed soap while being in a state of Ihram, and one who does so is obliged to fast, give Sadaqa(charity), or offer a sacrifice in expiation: He/she either fast for three days, feed six needy persons from the Haram area(one kilo of rice for each), or sacrifice an animal within the boundaries of that area and divide it amongst the poor and needy there. However, it is permissible for him/her to offer fasting after going home.
• Is it permissible to offer an absentee funeral prayer?
Yes, it is permissible to offer an absentee funeral prayer.