It is possible to cast objects of abstract classes

I think you have already answered only, but I put it in a more formal way.

The same thing you see more clearly with the classic example zoo

abstract class Animal {...}
abstract class Mamifero extends Animal {...}
abstract class Ave extends Animal {...}
class Aguila extends Ave {...}

As expected:

Aguila a= new Aguila()
if (a instanceof Ave) {
   ... //entra
}
if (a instanceof Animal) {
   ... //entra porque un Aguila es un Ave, que es un Animal
   Animal an = a; //no hace falta ni hacer casting, es implícito por ser seguro
}
if (a instanceof Mamifero) {
  ... // aqui no va a entrar
}

Animal an = new Aguila() //funciona

Aguila ag= (Aguila) an;
//funciona pero, como restringes, hace falta el casting explícito.
// (decir que es un Aguila es más restrictivo que decir un Animal)

The last assignment has demanded an explicit casting to force you to tell the compiler I know what I'm doing . That is, not all animals are eagles but I know that in this case it is like that and I can force it.

Mamifero m= (Mamifero) a;  //no te deja, en ningún caso un Aguila es un mamifero

In the first example, you are casting two classes (sisters) that come from Graphics then, that is, both classes have common properties but they are not the same as casting, so it's wrong.

The second case leaves you because you are defining the Grafi class as a Graphics class and it lets you cast it because Graphics is a parent of Graphics2D.

In summary, the abstract classes can be inherited but you have problems to understand the inheritance take a look. My advice is ...

  

Always casts children to parents and never casts from parents to children, unless you are very sure that parent class contains the necessary properties to be able to cast the child correctly.