Because the interface declares the supeclass and the superclass from which your class inherits, these things can be omitted from the implementation file. This reinforces the concept of the implementation being purely devoted fleshing out the methods. The NSObject class takes care of this. The following sections will go into more detail about creating new objects. Instance variables can be referred to in your method definitions directly.
All instance variables are within the scope of each method without explicitly saying so.
It is also possible to have local variables with more limited scope within each method. If I may go out on a limb, you could say that anything that applies to standard C functions, also applies to methods of a class. New objects are created by sending an alloc message to the class object of the class you wish to make an instance of. Once a new instance has been created we must also initialize its instance variables. This is done by issuing an init message to the newly created object.