The way that I've done SQL backups and restores before is using phpMyAdmin, which is built into most hosting control panels. You may have to create each database manually in your control panel, depending on which one you use.
The search & replace tool works automatically, but you need to tell it what it needs to replace. As an example, you might want to change 'http://www.mysite.com' to 'http://site1.mysite.com'. Enter those values in when it asks you to, and it will do what it needs to.
