An Abstract Class may and may not have abstract methods but an interface has unimplemented methods only. So what is the difference and advantage of using an interface if my abstract class has all of its methods marked as abstract?
An Abstract Class allows for "partial implementation" (see the template method pattern), but in this case, if all methods are abstract, you don't see that benefit. One other thing you can do is include fields, you're not just limited to methods.
Remember, there's a conceptual difference between an "abstract method" and the contract defined by an interface. An abstract method has to be overridden by a subclass which is done through inheritence implementation. Any polymorphic calls (downcasting) will require one superclass per class or it would hit the diamond inheritance problem. This kind of inheritence based tree structure is typical of OO design.
As a contrast, an interface provides a signature of a contract to fulfil. You can fulfil many interface's needs as long as you retain the signature as there is no question of going back up the class hierarchy to find other implementations. Interfaces don't really rely on polymorphism to do this, it's based on a contract.
The other thing of note is you may have "protected" abstract methods, it makes no sense to do such a thing in an interface (in fact it's illegal to do so).