To your last question that would depend entirely on their fee agreement.
To the first question, your file with the attorney is yours, like medical records are yours. So when you leave the attorney you are entitled to your file that includes all the factual stuff about the case.
Work product (notes, legal research, etc) belongs to the attorney, and may or may not be turned over. Some states require it, some forbid it, and I have no clue where NJ stands on this.
Nagel never answered it.