Hi Joseph, welcome to the forum.
It can take up to 72 hours for the new DNS information to propagate across the Internet, during this time your domain may 'come and go', before settling down.
Generally not. They may (but probably won't) email you to let you know the changes have been made, but since they have no real way of knowing that the new DNS information has fully propagated, they can't really email you concerning that.
Basically, it is just a matter of being patient and waiting for things to start working. Although, it is probably a good idea to add the domain to the DreamHost hosting system in the panel at Domains -> Manage Domains -> Add New Domain / Sub-Domain, unless it already appears in the domains list.
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