Seeking advice for action on speeding ticket in NJ,USA.

Hello Everyone,
I was stopped by the traffic police on a highway for over speeding recently. The officer asked if I had any points on my record and I said i have been a safe driver and this is the first time i have been stopped for any violation. The office said that i was driving at a speed of 83 miles in a 65 miles zone. I explained the officer that I was in the extreme left (fast lane) and i was following the traffic speed. He said since it is my first offense he gave me $50 ticket and 4 points on my record. I called the court this morning to see if I can get the points eliminated/reduced. So my queries are:

1. Has anyone in NJ been in such a situation and got their points eliminated from the record by requesting to the judge/prosecutor at the hearing?

2. Although my ticket does not say that I have to visit the court and i can pay online, would going to the court make any difference if I apply for GC in the future? (I believe there is some Q in the GC application that asks if you were asked to come or if you visited the court.)

3. Does having traffic tickets make any impact on GC application? Considering with the recent law change in UK, I believe this might be a pertinent question.

Please provide your feedback.

Thanks,
Marian.

Can anyone please put some light to my query?
thanks.