The first thing we need to see is a traceroute or some other piece of information as this post (although lengthy) is rather devoid of any useful information.
If you are seeing 10.x IP's either A)
You have manually done this on your own internal network, B)
You are for some reason seeing the internal IP assigned by the DOCSIS router to the modem, or C)
you are confused.
Being able to see the actual router interfaces isn't surprising either. Some companies name the hops after the interface they are connected to. For example "rc2ar-ge9-1.ed.shawcable.net [220.127.116.11]" appears on a traceroute from my house. This is because the actual port is named rc2ar-ge9-1. Is this similar information to what you are seeing?
As for your (from what I understand you are running) DNS server being refused I am not surprised. Are you sure you have put in the proper IP address? Why not just use Google's 18.104.22.168 if you are having so many issues with your ISP? Again with the whole NOTAUTH response you seem to be receiving...I have never heard of someone running a NOTAUTH server, NOTAUTH is a DNS response given when a DNS server is attempting to update a zone in which it is not authorized to do so (which in your situation would be proper as your ISP will not allow a user to update DNS records. I that were allowed then anybody could make a DNS update that says microsoft.com should point to 22.214.171.124)
Also 10.22 I see something microsoft related and 192.168.64 I see something as well.
The only reason you would be able to see 10.22.x.x and 192.168.64.x at the same time is either A)
you have 2 network cards, or B)
you have your subnet mask set to something invalid like 126.96.36.199 (which I am pretty sure would not work)