Note: If a constructor does not explicitly invoke a superclass constructor, the Java compiler automatically inserts a call to the no-argument constructor of the superclass. If the super class does not have a no-argument constructor, you will get a compile-time error. Object does have such a constructor, so if Object is the only superclass, there is no problem.
I don't like it when people add an explicit super() call (with no arguments), because it is superfluous:
If the superclass does not have a no-arguments constructor, then you must explicitly call super(arguments) in each subclass constructor.
Simply: yes. You must initialise all the fields, so as to create your instance in a consistent state, ie fulfilling its class invariants. The only instance where you can get away without a super(...); call is if the superclass has an accessible no-arguments constructor. One must presume that constructor will put the superclass object into a consistent state.
I think the only state in which case it is good design not to initialise the fields in the superclass is when the superclass hasn't got any fields!