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.
                             
                        
                            
                                
                                Does Istigfar (Asking Allah for forgiveness) between the first and the second part of Friday prayer`s sermon render the prayer invalid?
                                Talking during Friday prayer`s sermon is disliked, but there is no harm in offering Istigfar between the two parts of the sermon, and it doesn`t invalidate the prayer as it is actually from Sunnah. And Allah Knows Best.
                             
                        
                            
                                
                                My headcloth is causing me a terrible headache and severe shortsightedness. Is it permissible for me to take it off?
                                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.
If the headcloth Khimar is harmful, it is sufficient to wear the Niqab (face-veil). However, with the passage of time you will get used to the Khimar and these symptoms will go away. And Allah The Almighty Knows Best.
                             
                        
                            
                                
                                Is it permissible for a Muslim woman to wear trousers at home?
                                Wearing trousers at home isn't prohibited so long as non-Mahrams do not see her. And Allah Knows Best.