NAT - Network Adress Translation.
If you're behind a router. The router gives you internal ip adresses such as (10.x.x.x or 192.x.x.x and so on). What NAT does is to translate the local ip to your public ip. So even if you're on the local adress 192.168.0.2, when you surf the web it will say your public IP and not the local ip. This is a basic firewall feature.
Sure all NAT ports are open in the common userbased routers. If not then you would need to open up port 80 in order to be able to surf the web and so on.
In order to allow incoming connections (as a host) you need to open ports 6073,6100-6200 in your router. As you might see, you need to specify hostname/local ip there. This is called SAT. Incoming traffic doesn't know to which local ip it should go to. All it knows is the public IP adress. The router will look for the destination port in its port forwarding table. It will see that the port 6073 traffic should go to the 192.168.0.2 adress (this will be the computer with the demigod client running).
Anyone that can help me with the NAT Facilitator message?
Forget NAT or SAT. Let's just say I've opened ports 6073,6100-6200 to my computer in my router. I've got no software based firewall at all. Windows Firewall is turned off.