Is washing the private part after urinating (Istinjaa`) a condition, and is it done with water and soap, or with water only?
                                Istinjaa` is obligatory for removing impurity, and it can be done with toilet paper, or a stone, or water. It is preferable to do Istinjaa` first with paper, or stone, or the like, then to wash the private part with water until making sure that the impurity has been removed. Using soap is not a condition, but there is no harm in doing so provided that it is washed off with water. It is also permissible to use either water, or paper if impurity is removed by any.
                             
                        
                            
                                
                                A woman has asked her husband for Khulu`, her gold, deferred portion of the dowry and furniture. Is she entitled to that, knowing that her husband doesn`t want to divorce her?
                                All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
Khulu`* can`t takes place save before a judge of Sharia and he has the authority to make the suitable decision in this matter. And Allah The Almighty Knows Best.
* Khulu' is when parties agree to separate by way of consent, usually upon terms such as the wife agreeing to repay her Mahr (dowry) to the husband upon him agreeing to grant Talaq. The iddah period (waiting time after a divorce) of a woman who seeks a khula, is one menstrual cycle or one month if she is post-menopause i.e. ceased menstruating. This is to ensure she is not pregnant. This differs from when a man gives a talaq; the iddah period is three cycles or three months.
                             
                        
                            
                                
                                Although engaged to be married, a man committed adultery with another woman. What is the ruling of Sharia on this?
                                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.
 
There is no sin on the woman to whom this man is engaged; however, he is considered a cheater and must receive the punishment prescribed in Sharia. And Allah The Almighty Knows Best.
                             
                        
                            
                                
                                Does Husband fasting while being impure for having sexual intercourse with his wife at night permissible?
                                Yes it is permissible for you to fast because impurity isn't among valid fasting conditions, but you are obliged to perform ritual impurity in order to catch up Fajr prayer at its due time. And Allah Knows Best.