Yes, you have to pay the NJ taxes owed with out of pocket funds, it CANNOT be paid from the federal tax refund.
In the File section of the program on Step 2, with state taxes owed, you were given several options on how to pay the taxes owed. What did you choose?
Yes you must pay your state taxes owed directly to the state. There is no way to apply some of your federal refund to pay your state taxes owed. Most states have extended the deadline for paying state taxes to July 15, 2020. You should check the New Jersey tax department web site to confirm the deadline.