I can understand why you are confused. When you register a domain name through DreamHost, under an account with no active hosting plan, the situation can become complicated due to the fact that DreamHost does not provide DNS for the domain, only registration. Unfortunately, if you want DreamHost to host the DNS for the domain, you will need to purchase a hosting plan.
No, you own the domain name, DreamHost is simply the registrar.
See above; DreamHost does not supply DNS hosting for the domains registered here, unless you also have a hosting plan under your account.
Usually the company providing the hosting for your domain will also provide the DNS, you just set the name servers for your domain (at your registrar) to point to the name servers of the hosting company that you are using.
If you are stuck for DNS, I believe ZoneEdit provides free DNS services. Note, I have not personally used these services.
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