Sorry Coffee, you have some weird issues there
The DNS name is because W2K3 uses DNS as internet format names, since you probably didn't specify one, it created one for you. You could have put (and still can) any DNS name, as long as it resembles a DNS entry, for example coffeedomain.int (using int for internal, since it is not a Internet DNS)
This is as example. not sure about the steps for changing the DNS, but I am guessing you could just change the name, delete the database and force an update, or just change the name and ask for a new harvest (update)
NAT on the same server as AD...humm, not sure if you want to do that, unless you are experimenting and trying new things. With time it would slow down the computer. Get an old PC and install NAT there. There are lots of solutions using Linux which are pretty good, more advance, and feature packed. One recomendation to look at Linux Enbeded Appliance Firewall
It took me a long time to find this I couldn't remember how it was called and had to go thru THG archive
Since I did that, I also recomend Auditor Security Collector A lot easier to install (no installation)
THG also has a 2 part (so far) guide for installing W2K3. I haven't read them yet, but you might want to take a look to see if there is any usefull info.