I want to make sure of travelling during NIW filing.
With my J1 VISA, can't I travel around until NIW is finalized?
If I want, should I get AP and then it might negatively affect my J1 visa status after J1 waiver?
You can travel on your J visa before and after your I-140 (NIW) is filed. You will only need the AP once you file the I-485*. Please note that you must have a valid J-visa stamp as well as your passport to be able to travel on your J visa. You should also bring a copy of your DS-2019 with you when you travel.
*When you file the I-485, you should simultaneously file the I-131 to get an AP. Filing for and receiving an AP does not invalidate your J-visa status. However, when you actually use the AP to re-enter the U.S., your J-visa status will be invalidated.
No, you cannot use a J visa stamp to reenter the US after international travel once your I-485 is filed. You must use an AP to reenter the US once your I-485 is filed. If you use a J visa stamp to reenter after your I-485 is filed your I-485 will be deemed abandoned and you will lose the I-485 filing fee.