I need you to be more specific in your question(s) if you could. When we answer general ones like "what do I do", "what are my rights", or "what are my options", we have to give general answers and, invariably, the customer responds with "I already knew that". This type of forum works better if you ask specific questions so we know exactly what you are looking for.
As to the amount of time involved, in NJ it is a little strange since the time limits can vary slightly as opposed to other states where they are set in stone. In general in NJ it takes about two to three weeks to get a court date as you have seen. Then if you don't show up for court or if the landlord prevails on the merits at court, it usually takes about seven to eight days for the paperwork to be prepared and for the landlord to take the next step and file for a warrant for removal.
When that is filed the sheriff or other officer will go to the residence within a day or two and post the warrant to give you three days after which the sheriff/officer will return to evict you.
At any time during this process a tenant can file for an order to show cause to stop the process for a legitimate reason (ex. you didn't receive notice) or you may request a hardship stay which is not normal and the courts rarely grant the request but if the court did grant the request it would give you another six months before you had to be out.
If your question has been answered then I'd offer my best wishes to you and ask that you please not forget to leave a Positive Rating so I receive credit for my work.
Of course, please feel free to ask any follow up questions in this thread. I want to be sure that all of your questions are answered. In addition, once you issue your Positive Rating the question will lock open and no longer time out so you can come back to it anytime in the future if you think of any follow ups.