I’m assuming you mean your existing web site, zenphoto and forum are already hosted at DreamHost.
As for as the databases go - its just like email sorta, it doesn’t matter where your database client is as long as you use the same details to access the database.
I’m not sure what setup your looking for. Generally you have a hosting plan, and you have system users for this plan, and when you host a domain for web site access, you get to specify a directory controlled by a system user.
For example, If you started with user “bob” and domain “example.com”, then web site files for http://example.com/ would be served from /home/bob/example.com
Say you want the gallery on a subdomain, ie “photos.example.com” but you want to use “bob” to manage the files. Then the gallery would go in /home/bob/photos.example.com
An alterntaive would be to create a second user, “ansel” and specify that “photos.example.com” be served from /home/ansel/photos.example.com - but you have to login to ansel instead of bob to manage the files.
Once you know what system path the gallery is going to be served from, generally you can simply log into shell and use a few commands to copy the files from one path to the other. This works given both users are yours and on the same machine. Otherwise you have to use a file transfer program like rsync - which you can run from one dreamhost machine to another instead of using your own computer as a middleman.