Is a menstruating woman obliged to pray during menses, and should she make up missed prayers?
                                All perfect praise be to Allah, The Lord of The Worlds                                                                                                                                                                        A menstruating woman is prohibited from prayer during her menses, and she isn`t obliged to make up missed prayers. And Allah Knows Best.
                             
                        
                            
                                
                                Does passing wind, from the anus without a smell, invalidate prayer?
                                If a person is certain of having passed wind even if it was with no smell, then both his/her ablution and prayer are invalidated, thus he/she should remake ablution and re-perform prayer.
                             
                        
                            
                                
                                 If a disposable water bottle has the logo (Al-Aziz Water Shop) ,is it allowed to throw it away considering that (Al-Aziz) is one of Allah`s beautiful names?
                                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.
You can remove some of the letters so that the word isn`t read as (Al-Aziz). And Allah The Almighty Knows Best.
                             
                        
                            
                                
                                Is prayer mandatory on a dying person who goes through a state of unconsciousness, then wakes up?
                                If he wakes up and was conscious, then he should pray the way/manner he could, but if he wasn't, then he is exempted from obligatory prayer as Allah Says in this regard (What means): "On no soul doth God Place a burden greater than it can bear." [Al-Baqarah/286].