Option #2 fulfills the conditions of the hashcode contract:
(1) Whenever it is invoked on the same object more than once during an execution of a Java application, the hashCode method must consistently return the same integer, provided no information used in equals comparisons on the object is modified. This integer need not remain consistent from one execution of an application to another execution of the same application.
(2) If two objects are equal according to the equals(Object) method, then calling the hashCode method on each of the two objects must produce the same integer result.
(3) It is not required that if two objects are unequal according to the equals(java.lang.Object) method, then calling the hashCode method on each of the two objects must produce distinct integer results. However, the programmer should be aware that producing distinct integer results for unequal objects may improve the performance of hashtables.
So '0' response will work here since its consistent (condition 1), it always produces same hashcode for equal objects (condition 2), and though it produces same hashcode for unequal objects it is tolerated by the hashcode contract (condition 3).
For 2nd question there are no arguments to be passed in hashcode() method.