You may want to check out njgunforums for more specific advice, but here's what they will probably say:

1. There's really no way for anyone to prove where you were gifted those firearms, but if it happened in NJ, you and your friend were required to have a Firearm Purchaser Identification Cards (FID) and fill out a Certificate of Eligability. The form isn't sent to the state. It is kept by both parties to prove a firearm was lawfully transferred from one eligible person to another. If you acquired them while living out-of-state, no paperwork needed as long as they're NJ legal (not stolen or "assault weapons").
2. That's a judgement call, not specifically a legal one in NJ. Ask yourself, "even if empty, would I be comfortable with my friends/family/kids playing around with them?" If not in a gun safe, they really should at least be in a locked up in a closet or gun case.
3. You really ought to go through the process to get a FID first. The FID is also used to purchase handgun ammunition in NJ, so if your rifle uses ammo that is commonly also used in pistols, you may need one if you choose to purchase ammo in-state. While in many situations a FID is not specifically required, it does prove that you aren't prohibited from possessing a firearm in NJ, and that may make others (law enforcement/gunsmiths/shops) more comfortable when dealing with you.

Just remember, transporting firearms in NJ needs to be done directly and discreetly. Locked and unloaded in the trunk or other container. No intermediate stops. So if you're going hunting/to the range/to a gunsmith, you're really not supposed to stop off at a Wawa along the way.