Is it permissible to pray with a heater (stove) in front of me?
                                There is no harm in praying with a heater in front of you, as long as you do not intend to venerate the fire or imitate those who worship it. And Allah Knows Best.
                             
                        
                            
                                
                                My father passed away before my grandfather. Am I entitled to any share of my grandfather`s inheritance?
                                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.
According to Islamic courts, you are entitled to what is called obligatory bequest (The distribution of estate to grandchildren who has either lost a parent before the death of the grandparents). Therefore, if your grandfather left such bequest for you, then take that share or else it is more prudent to take nothing. And Allah The Almighty Knows Best. 
                             
                        
                            
                                
                                Is it permissible to give my zakat to my grandson who is studying at university, while I am living abroad and my money is in my home country? Also, is it permissible to assign my father the responsibility of distributing the zakat to the people in my home country?
 
                                It is permissible to give zakat to a son whom his father is supporting if he is an adult and in good health, because his father is not obligated to support him, making him one of the poor among the Muslims. However, the student who may receive zakat is one who is diligent in seeking beneficial knowledge for the Muslims and is religious. Zakat should be paid in the country where the money is located, and appointing your father to distribute the zakat in the country where the money is is the correct approach. And Allah Knows Best.
                             
                        
                            
                                
                                Is it permissible to openly announce the engagement of a woman who is in her waiting period (iddah)?
                                It is not permissible to openly announce the engagement of a woman in her waiting period (Iddah), but it is permissible to hint (imply) at it if she is in her waiting period after the death of her husband. And Allah Knows Best.