Does the time of Fajr (dawn) prayer start after the first Athaan (call for prayer), or the second one?
                                All perfect praise be to Allah,The Lord of The Worlds                                                                                                                                                                    The time of Fajr prayer starts after the second Adhan. And Allah Knows Best.
                             
                        
                            
                                
                                I made a vow "If the Israeli troops retreated out of Gaza strip I will buy a cake from a certain bakery" and it happened. Am I obliged to buy from the same bakery?
                                You are obliged to buy from the same bakery. And Allah Knows Best.
                             
                        
                            
                                
                                What is the ruling on a person who broke the fast a day in Ramadan due to hardship?
                                He/she is obliged to make up that day.
                             
                        
                            
                                
                                Is everyone obligated to follow the fatwas of his country, and if we adopt the fatwas of scholars of other countries, is it considered a sin?
                                All perfect praise be to Allah, The Lord of The Wolrds and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.
It is permissible for the person who isn't specialized in Sharia sciences to apply the opinions of renowned scholars whom he trusts ,whether they be from his own country or not ,but if the scholars have different opnions regarding a certain issue/matter, then he must consult someone who is more knowledgeable than himself .It is preferable that you (the questioner) specify the case of your interest ,so that we could give you a more specific answer since some scholars deliver fatwas based on illogical/atypical opinions which should not be applied no matter what .And Allah The Exalted Knows Best.