I got into a car accident (I was at fault), did minor damage to the car in front of me. I will be liable, no one was hurt. Will this incident add points to my license (NJ)?
Only if you were issued a ticket for a moving violation in connection to it. Your insurace rate, on the other hand…
Not sure about NJ, but in FL an accident is worth an additional point. So instead of 3 points for running a stop sign, you get 4 points deducted. But that’s only if you got a ticket.