Is a woman`s face an Awrah (a private part) that should be covered?

During prayer, a woman`s whole body is a private part except the hands and the face. Outside the time of prayer, scholars agree that a woman should put on her Islamic wear to avoid temptation.

Is it permissible for the woman to use her mobile phone while on the street?

Modesty should be observed by the woman at all times, so she is free to use her phone while on the street as long as it is done within the limits of Islamic manners.

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.

 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?