None of this information will be considered pertinent to the charge itself and unfortunately these omissions probably will not merit a dismissal of the charge. The ticket sets forth who you are and what you allegedly did wrong and that is likely enough for any court.
A public defender won't be available for a minor violation like your speeding ticket. It's four points potentially on your license. You may certainly benefit from assistance of a private attorney but whether the worked for you would be a combination of financial considerations and a look at your potential liability in the case. Most attorneys should offer free consultations to at least help you determine your best course of action
Judges have to make that call--who is telling the truth. Without any evidence beyond the verbal testimony of each party, it's up to him to decide and there's really not much someone can do to get it overturned on the grounds that he made the wrong decision. That's a big part of what judges do in cases like this--"judge" the veracity of the testimony they hear.
It's a 2 point ticket in NJ. No one can every 100% predict what an insurance company will do but if this is the policy that covers the cars you drive and you are listed on the policy then certainly your driving violations can push the rates up
Visible issues like this (those you can see on a reasonable inspection of your car) are generally going to be the driver's responsibility, not the dealer or the owner if a non-owner was driving. You can always contest the ticket like any other.
Where you live, your age, the policy, the insurer, car you are driving...all are part of the equation along with your driving history. There's no way to know exactly what may happen to your insurance, except to say that convictions won't be good for it (speeding worse than the disobey a traffic device) and the defensive driving class may help offset to some extent any damage done by convictions.
We're always going to advise to plead not guilty. Even if your record is perfectly clean and a ticket relatively minor, you still need to be concerned with keeping your record as clean as possible going forward. Perhaps a plea bargain can be negotiated with the prosecutor.
Note that 72/55, even with a perfect driving record, is enough under the NYS Insurance Laws to warrant an increase in insurance rates. I'm not saying it will happen but it's certainly something to consider.