
To the best of my knowledge only NJ residents who own firearms need to have a state-issued, 'FOID'.
Based on the years I lived in NJ the answer to your question is, 'Yes'. However, you have to transport your firearm in the state's approved manner. Here's what I remember: The gun has to be unloaded and retained in a locked or securely tied case that is not readily available to the occupant(s) of the vehicle. Ammunition has to be separately stored, again, in another secure package. (You may NOT transport loaded magazines.)
It gets dicey where certain firearms and components are concerned. NJ does not allow any magazine over 15 round capacity; and many, 'assault rifles' are illegal to possess in NJ.
You may only transport a firearm under specific conditions which mainly include either to or from a gunsmith or shooting range. I do not believe, 'I'm going to a friend's house; and I want to show him my gun.' or, 'Because I wanted to keep my gun with me.' are acceptable legal excuses.
Based on one case that I am familiar with, it is allowed to transport a firearm through the state. This is good to know if you live in PA and must use a part of NJ to complete your trip. What kind of firearm you transport through the state, and whether or not you stop in NJ while transporting a certain type of firearm may be another story, though.
Hollow points are legal to own and use in NJ for everything except the commission of, 'a crime'. The problem is exactly, 'how' do you define a crime? Sometimes shooting at a protagonist may constitute a crime; consequently, it's not a good idea to use HP's for self-defense in NJ because it could bring an additional charge.
That's, pretty much, what I remember about using and transporting firearms in my old home state.