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#11
Woah, hold on there .
So, what you had heard is partially correct - Active Directory (any server version, any domain or forest level) absolutely requires DNS to work. Everything in active directory itself relies on DNS in some way, shape, or form, and without it AD doesn't work, computers can't authenticate, join the domain, etc. So, yes, DNS is required for Active Directory to work, and that is why you really want to install the DNS server role on your server before you install and enable the Active Directory role (the AD installation wizard will configure DNS properly for you after asking you a few questions about your domain).
However, having a DNS domain does not have anything to do with the internet - in fact, almost every AD domain out there in existence doesn't have any integration with internet-facing DNS servers short of forwarding or discovery. Also, using a root-level DNS domain for an internal domain structure, unless you are using it specifically for that purpose, is neither recommended nor a good/best practice. For example, if you owned the domain "mydomain.com", and you wanted to use that for Active Directory, that would break things like www.mydomain.com, unless you added an A record into DNS manually (or actually had a host called www in your domain - also not a good idea, in either case ).
What you should be doing, is using the name of a new subdomain of "mydomain.com", perhaps called "ad.mydomain.com", when you set up your AD infrastructure. That will create an Active Directory Forest root called "ad.mydomain.com", and the netbios domain name (unless you changed it) would be "AD". You could then easily create child domains in this forest later (for example, "sales.ad.mydomain.com" or "marketing.ad.mydomain.com") as necessary. Again, NONE of this has anything to do with the public "mydomain.com" other than you are now using it as part of your DNS naming structure for AD.
Hopefully that makes some sense - if it doesn't, I strongly suggest doing a little more reading/research into AD itself, as these are pretty basic questions about the foundations of Active Directory.
How DNS Support for Active Directory Works: Active Directory