Is speaking to a person from the opposite sex forbidden or not?
                                All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Talking to a person from the opposite sex is forbidden in Islam because it entails a great deal of evil, which could lead to a graver sin. Moreover, Islam forbids having a friend from the opposite sex. And Allah The Almighty Knows Best.
                             
                        
                            
                                
                                What is the ruling on having brotherly ties between a strange man and a strange woman, and is the former considered a Mahram (unmarriageable) to the latter?
                                Such a relation between a strange man and a strange woman is forbidden in Islam because it involves forbidding what Allah has allowed by marriage, and allowing what Allah has forbidden such as looking and the like. Such a relation doesn`t render any act lawful between them, thus they are forbidden to look at each other, have a Khulwah (seclusion), and travel together.
                             
                        
                            
                                
                                Is prayer nullified by nose bleed?
                                 All praise be to Allah, The Lord of The Worlds.                                                                                                                                                                           Blood coming out of the nose, or a wound doesn`t nullify prayer regardless of its quantity. And Allah Knows Best.
                             
                        
                            
                                
                                 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.