It's two points worst case scenario.

I was pulled over by NJ trooper who said he had call(s) about my driving...on hearsay

Hire a lawyer. You were pulled over based on an anonymous tip. There's no way you can file the motion to suppress and argue the applicable case...

Improper passing in a button or marker?

If I understand you correctly you received a ticket for improper passing because you cut a car off or something like that to get onto a highway but...

My question is: Can my son just pay the ticket or should he go to court?

You shouldn't have a concern bc there are no collateral consequences such as points surcharges etc. associated with this ticket.

Can an officer mail me a ticket after stating on record (I recorded) that he gave me a break?

Since he did it within thirty days it's within Statutes of limitations. He changed his mind or a supervisor did it for him probably because he...

Can't speak in a vacuum. Must know the facts of the case. Statistically these days the prosecutors win approximately 70% of their cases. ...

Should i plead guilty or not ?

Prosecutor is not allowed to downgrade your charge because of your license status so your option is to pay it or to have a trial.

In new jersey does a cop have to let you know that their body cam is on and recording you during a vehicle stop?

Your description is not related to your question but Officer doesn't have such an obligation by law.

Can I be cited for careless driving in an accident at night where the other driver involved did not have headlights on?

It may not had lights on but it wasn't invisible. Anyway, if you take the case to trial then you would need to subpoena the other officer to...

How can I get a ticket in the mail for driving with no license without being pulled over and I don't own a car?

It's possible the cop knew you from prior interactions and saw you driving and mailed you the ticket because he had something else to do.