What is the difference between Tahajjud prayer and night prayer, and do they have a particular Witr prayer other than that of Isha (evening prayer)?
                                Tahajjud and Qiyam-Al-Lail (night prayer) are two words for the same meaning which is offering voluntary prayer at night after sunset, but before dawn break. However, Tahajjud is offered after waking up; whereas, Qiyam-Al-Lail is permissible before sleeping, or after it. Therefore, every Tahajjud is a Qiyam, but not every Qiyam is a Tahajjud. Moreover, there is no specified Witr for both of them, but Witr after Isha is by itself the Witr of Qiyam, and it is a Sunnah to postpone it until after Qiyam if the worshiper thought that he was most probably going to wake up in order to offer it, but if he wasn`t sure of waking up, then he is at liberty to offer it before going to bed as was reported in the Prophet`s Hadith.
                             
                        
                            
                                
                                A sixteen-year-old young woman suffers from Alopecia, and lost her hair and eyebrows as a result. Is it allowed to draw her eyebrows using henna and an eyeliner? 
                                All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
It is permissible for women to use henna and what the asker has mentioned isn`t considered hair extension. However, if this young woman is proposed to, she must disclose this matter to the person proposing to her to avoid deception. And Allah The Almighty Knows Best. 
                             
                        
                            
                                
                                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 a woman to offer the obligatory prayer after Adhaan (call for prayer), and before Iqamah (The announcement that the prayer is about to begin) in the mosque?
 
                                Yes, it is permissible for a woman to offer the obligatory prayer immediately after the Adhan and before the Iqamah in the mosque. And Allah Knows Best.