In NJ, is an executor responsible to give a yearly report and if so, how often. (The owner of the estate is alive)

If the owner of the estate is still alive, there is no executor.  There is a document naming an executor, but one is not appointed until the person who wrote the will dies, and the will is admitted to probate.  The executor must qualify and then letters are issued indicating the person is the executor.  The person who writes the will has the right to change it up until the day they die, so there is no executor, and there is no estate, until the person dies.