Does an interface by default extend Object?

Every class implicitly extends Object and so inherits every (non-private) method of the Object class.

Every instance has a class and therefore has all of the method of Object.

Whether an instance implements an interface or not is completely irrelevant to this point.

Object is a class, and interfaces can not extend classes, so "no" - the interface doesn't inherit anything from any class.

Then from where the equals method come, is the interface also extends the super class Object ?, if that true how an interface can extends a class?

The Java Language Specification deals with this explicitly.

From section 9.2:

If an interface has no direct superinterfaces, then the interface implicitly declares a public abstract member method m with signature s, return type r, and throws clause t corresponding to each public instance method m with signature s, return type r, and throws clause t declared in Object, unless a method with the same signature, same return type, and a compatible throws clause is explicitly declared by the interface.

Basically, this is so that you can use equals, hashCode etc - because the way that the Java language is specified means that any concrete implementation of the interface will be a class, and that class must ultimately be a subclass of Object, so the members will definitely be present.

To put it another way, while the interface itself doesn't extend Object, it is known that any implementation will.

Here the class A no need to implements the method toString() as it's present in Object class. Then what is the objective of defining those method in collection interface as they can't force there implementation class to implement those method.

Usually this is just done for clarity, e.g. to document what is expected of an implementation in terms of the members declared in Object.