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.
                             
                        
                            
                                
                                Are all the children of a suckling woman considered brothers to the strange child whom their mother had breastfed, or just to the one who had suckled with him?
                                All the children of the woman who had suckled a strange child are considered his/her brothers and sisters.
                             
                        
                            
                                
                                What is the ruling on someone who perform their prayer after finishing it because they believe they missed a Rak'a, a prostration, or that they did not perform it correctly (thinking their prayer was invalid)?
                                If he was sure that his prayer is void then reperforming it is an obligation along with figuring out the reason of invalidity so long as this wasn't out of uncertainty. And Allah Knows Best. 
                             
                        
                            
                                
                                What should one who made an intention, at night, to make up for a missed fasting day, but broke his fast on the next day?
                                One who started making up a missed fasting day, then broke his/her fast without a legitimate reason is considered sinful, and is only obliged to make up for the missed fasting days. And Allah Knows Best.