If a class were declared private, no one could access it, including the runtime. Therefore the class could never be instantiated.
If you were to remove methods and fields from a subclass, then the subclass could no longer be used as an instance of its superclass. In fact the subclass might not have any relation at all to the superclass if all the superclass's methods and fields were removed.
An interface can be implemented by a class which is already a subclass of another class. A class which is already a subclass of another class cannot extend an abstract class as well. Furthermore, an abstract class can contain non-abstract methods. An interface cannot.