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.
                             
                        
                            
                                
                                What is the ruling on memorizing the Quran during menstruation, knowing that I do not read directly from the Quran but from a paper or from my phone?
                                It is not permissible to memorize the Quran during menstruation because memorization requires repetition, and a menstruating woman cannot touch the physical pages of the Quran. Similarly, if the Quranic verses appear on the screen of the phone, it is considered like touching the Quran. And Allah Knows Best.
                             
                        
                            
                                
                                Is it permissible to listen to chants praising the Prophet if accompanied by musical instruments?
                                If singing, or chanting in praise of the Prophet was accompanied by a forbidden musical instrument, then it is forbidden.
                             
                        
                            
                                
                                I am a disabled woman who has vaginal discharges and can`t control her urine. Therefore, I combine prayers. Is that permissible?
                                All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all his family and companions.
According to the Hanbali doctrine, it is permissible for the sick to combine prayers. In your case (Asker), it is better that you delay the noon prayer until a few minutes before the afternoon prayer in order to minimize the time span between the two and perform each alone. In addition, you can do the same with sunset and evening prayers. Finally, we ask Allah to bless you with recovery. And Allah Knows Best.