Is data in an abstract class all abstract? code example

Example 1: is it necessary for abstract class to have abstract method

No, abstract class can have zero abstract methods.

Example 2: define abstract data type

Abstract Data type (ADT) is a type (or class) for objects whose behaviour is
defined by a set of value and a set of operations.

The definition of ADT only mentions what operations are to be performed 
but not how these operations will be implemented.