Is it incumbent on a father to cover the marriage costs of his son if the latter couldn`t afford them?
                                The son should seek the help of his relatives in order to convince his father to do the aforesaid, and the father should make sure that his son doesn`t commit fornication through helping him to get married, and Allah will reward him for doing so.
                             
                        
                            
                                
                                Is it permissible for the woman who is observing Iddah after her husband`s death to sit with her daughter`s suitor, although their marriage contract hasn`t been concluded yet?
                                All perfect praise be to Allah the Lord of The Worlds. May His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
A suitor who hasn`t concluded the marriage contract isn`t a Mahram*, so he must be treated as such. And Allah The Almighty Knows Best.
* The period a woman must observe after the death of her husband or after a divorce, during which she may not marry another man.
* In Islam, a mahram is a member of one's family with whom marriage would be considered haram, concealment purdah, or concealment of the body with hijab, is not obligatory; and with whom, if he is an adult male, she may be escorted during a journey, although an escort may not be obligatory.
                             
                        
                            
                                
                                Is Iddah (waiting period) incumbent on an old woman whose husband had died?
                                Upon the death of the husband, Iddah is incumbent on the wife regardless of their age. And Allah 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.