There were a lot of good questions on this thread, and many part answers.
NJ convictions "transfer/get reported to NY". However NY DMV does not record the violation. Therefor many attorney will tell you that the conviction transfers, however that is only part of the story. (If they are not NY lawyers they are not responsible to know what NY does with the information, all they know is that NJ MVC passes on the information)
In addition, being that NJ MVC hopes that someone else will record the conviction, they don't. That means that the conviction is only recorded in the local Court, and not at the NJ state level. This also means that the insurance agency will not find out about the ticket, being that they only check the state agencies, and there is no public computer access to the local Court Computers. (Unless you inform the insurance agency yourself, so don't!)
Therefor it follows that if you have a NY license in NJ, your tickets evaporate! In addition, lesser point tickets in NJ which you plead down to, cost more (usually) than the high point ones
You should be warned that if your speed is excessive the local Judge has the discretion to suspend your NJ driving privileges. Also if you ignore the ticket, the "scofflaw" suspension will carry over to NY as long as they have your name and date of birth