Based on how the NVR is configured (by default remote access is permitted), you do not need a static IP.  If you have the NVR set to PnP which uses a P2P protocol to reach the NVR, the app will find the NVR no matter where you are.  But this is accomplished by sending some data and details to the vendor so they know how to reach the cameras when you are not on your local WiFi; like a reverse proxy.  Some people do not prefer this for remote access so the go with the second option.  I use a personal VPN which does require that I have a static IP or use something like Dynamic DNS (DDNS) to access my local network while away.

This also depends on many other factors such as what you are or are not blocking from going out your network router.  You need to make sure the necessary protocols are permitted and there are no issues with internal routing or NAT that may get in the way of access.

Yes, you are right. If you don't want to the IP address of your camera changes casually, you can assign a static IP for it.
1. Log into your camera. Go to Device Settings -> Network -> General.
2. Select Static as Network Access.
3. Change IP and remember to click OK to save.