The term used to describe a class derived from a parent class, inheriting the characteristics of the parent while adding its unique characteristics, is Inheritance. In this scenario, the Manager class inherits properties and behaviors from the Employee class, which illustrates the concept of inheritance in object-oriented programming. Encapsulation involves restricting access to certain components, Data modeling is related to the organization of data, and Data hiding is a subset of encapsulation focused on concealing internal object details, none of which accurately describe the relationship mentioned in the question.

A class that inherits functionality from an existing class is referred to as a 'derived class'. The derived class, sometimes also known as a child class or subclass, inherits the properties and methods of the base class, allowing it to extend or modify the behavior of the base class as needed.

The class ANumber has a private member variable _number which is initialized to 7. The class has two constructors: a default constructor that does nothing and an overloaded constructor that takes an integer parameter and assigns its value to _number. When the statement ANumber mynumber = new ANumber(3); is executed, it calls the overloaded constructor with 3 as an argument, which sets the value of _number to 3. Therefore, after the code is executed, the value of _number is 3.

To restrict the availability of the member variable accessCount to the base class and any classes derived from the base class, the appropriate access modifier to use is 'protected'. This ensures that accessCount is accessible within the base class and any class that inherits from the base class, but not to other classes which are not part of the inheritance hierarchy. On the other hand, using 'private' would limit the member variable's accessibility only to the base class itself, and no derived classes would be able to access it.

Simulating the final design of an application in order to ensure that the development is progressing as expected is referred to as prototyping. Prototyping involves creating a preliminary version of a product to visualize and test its design before full-scale production. This helps in understanding, refining, and validating the design and functionality of the application, ensuring that the development process is on the right track.