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.    
                             
                        
                            
                                
                                What is the ruling on the existence of cattles' marketplace of (Sheeps, cows and chickens ) inside a graveyard?
                                Graves must be respected, and it is not permissible to sit on them or show any disrespect. Establishing a marketplace within a cemetery is undoubtedly a form of disrespect to the deceased and is not permissible. Such actions should not be tolerated. And Allah Knows Best.
                             
                        
                            
                                
                                Is committing Zina (Adultery and extramarital sex) without the intention of getting pregnant or deflowered considered full Zina?
                                All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
 
The Messenger of Allah (PBUH) says: "The eyes commit fornication, the hands, the feet, and the private parts." [Musnad Ahmad, P.3912]. Sheikh Shu`aib `Arn`oot graded this Hadith as sound. What you are asking about is far graver. Generally speaking,  sincere repentance erases sins, good deeds erase bad deeds, and fearing Allah stops one from committing this heinous act. In addition, the devil is man`s worst enemy and whoever surrenders themselves to the wolf will be eaten. And Allah The Almighty Knows Best.
                             
                        
                            
                                
                                My engagement to a young man was announced and blessed by both our families reciting Al-Fatihah. Is it permissible that I take off my Hijab in his presence?
                                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.
Reciting Al-Fatehah (The opening chapter of the holy Qura'n) to declare an engagement isn`t tantamount to a marriage contract and it isn`t permissible for him to see you without hijab or stay in private with you before the conclusion of the marriage contract. And Allah The Almighty Knows Best.