NJ permit paper..detach?

I got a driver's exam permit today
its a paper and has a detachable paper card which looks like a car registration
with a barcode on it

Do I carry the whole paper? or
Can I detach that card and carry that only?

I think the purpose of the detachable card is for you to carry that around

Is it a temporary thing while you wait for the real card? In my state, I get a paper print out that has my driving permit info, while I wait for the actual card.

I carried around the full paper.

I have a quick question having to do with NJ. When you go apply for your id or permit the application asks you if you are in this country legally. Although we don't have a legal status do we mark yes?

Yes
you mark as you are in this country legally

Thank you!