Mysql is also backed up on a regular bases by dreamhost, btu for whatever reason you can't access the backup on your own. If for some reason you need a mysql backup you'll have to contact support and ask them to restore it for you.
There's definatly no extra cost for any of the backups DH does.
I'm not sure about mailboxes. If the mail is being delivered to a regular user who has FTP access, which is not the case for the majority of my addresses, then E-mail messages would be sotred in the maildir direcotry (in your home area) and that is also backed up with the .snapshot mentioned in the K-base. For the regular E-mail address I would think DH also backs those up, but you'd probably have to contact support to get them.
Also, don't think that you have to resotre your own backups if DH has data loss. Just a week ago, they were uprading mysql on their servers, and for some reason one of the 30 or so machiens they upgraded had some major coruption - basically lost all of the data there. I got an E-mail from DH explaining what had happend, and that they were restoring from a backup 2 hours old and that it should be total restored in an hour max.
The same goes for your webspace. If something goes wrong, DH will restore the stuff for you.