Hello! Let's see if we can't answer some of your questions:
That will occur after you change the DNS settings for your domain, at your domain registrar, to point to the Dreamhost DNS server (ns1.dreamhost.com, ns2.dreamhost.com, and ns3.dreamhost.com) and the change has been distributed across the internet. Once you make the change at your registrar, it can take from a few minutes to several days for the "update" to be reflected across the whole internet. Some will get the change sooner than others, and there really isn't too much you can do to speed the process along, so you just need to be patient. With proper planning, however, your site should remain reachable throughout the process (see below).
No. In fact, if you leave the site "functional" at GoDaddy while you set it up at Dreamhost, the site should be reachable from one or the other of the host while DNS is being updated (those browsers receiving the updated DNS lookup will be routed to the Dreamhost site, while those waiting to receive the update will be routed to the GoDaddy site). You can always terminate the GoDaddy hosting a few days later, after all the DNS updates have taken place.
Yes, that really is the price, and you will have no set up fees for the 2-year hosting plan. You will also have no "domain transfer fees" from Dreamhost if you leave your domain registered at GoDaddy, or transfer that single domain to Dreamhost as the registrar. Remember that "hosting" and "registration" are two different services, and can be (they often are!) maintained with two different companies. I suggest leaving the registration with GoDaddy until your new Dreamhost hosting is set up for the reasons described above. You can always transfer it later.
Of course, you could have extra fees if you somehow manage to incur bandwidth or storage overage charges (which is *highly unlikely given the amount of space and traffic Dreamhost provides), but the "price" has no hidden "gotchas",
You can save additional money on that quoted price by using a Promo Code (they are all over this forum) that will allow you to save up to an additional $97.00 on your first year's hosting - which makes the deal even better (make sure you sign up with a charge card, and include the Promo Code where it is asked for on the sign-up screen).
Welcome to Dreamhost, and good luck!