Should a person feel pleased, or have a virtuous vision after offering Istikhara (guidance prayer) in order to do what he/she had offered it for?
                                The result of the Istikhaarah is not necessarily that a person sees something (in his dream), or feels pleased, but the most important result of the Istikhaarah is whether a person is enabled to do a given matter or not.
                             
                        
                            
                                
                                Is it permissible for a person, who vowed to offer two Rak`ahs (units of prayer) everyday for Allah`s sake, to do so after the Fajr (dawn) prayer?
                                In principle, a vow should be fulfilled as it was originally intended, and if its time lapses then, it should be fulfilled at any time because of the vow. Therefore, it is permissible to offer them after the Fajr prayer, and there is no prohibition in doing so. However, it is preferable for him to offer these two Rak`ahs at some other time to avoid the disagreement amongst the scholars in this regard.
                             
                        
                            
                                
                                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 it permissible for a Christian man to embrace Islam in secret and is it permissible for a Muslim woman to marry him?
                                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.
His embracing Islam in secret is between him and Allah; however, it isn`t permissible for a Muslim woman to marry him except after he declares his Islam and it is ascertained that he is sincere about that. And Allah The Almighty Knows Best.