I want to know why Python is not fully object-oriented. For example, it does not support private, public, protected access level modifiers.
What are the advantages and disadvantages of this? By these expressions, Python is suitable for what applications (Desktop, Scientific, Web or other)?
I think Python is designed to be a hybrid.  You can write in object oriented or functional styles.  
The hallmarks of object-orientation are abstraction, encapsulation, inheritance, and polymorphism.  Which of these are missing from Python?
Object-orientation is a continuum.  We might say that Smalltalk is the purest of the pure, and all others occupy different places on the scale.  
No one can say what the value of being 100% pure is.  It's possible to write very good object-oriented code in languages that aren't Smalltalk, Python included.
Python is useful in all those areas: scientific (NumPy), web (Django), and desktop.
Why is Python not fully object-oriented?