Working fine is relative - upgrade conversion can go successfully for one person, and not for another.
To answer you questions:
Can I have the test server in the same domain as the live server?
Yes you can host the two databases in the same domain, as long as the machine names and IP addresses are different you shouldn't encounter a problem.
Will the data convertion from SQL 2000 to 2008 work fine?
Yes, the conversion should be ok - though I went from 2000 to 2005, I don't know how going from 2000 to 2008 will go. It's the users that can really cause a problem here. If all you do is move the data over and possibly recreate the users the internal ID that SQL server uses to track the users will be different and prevent users from logging into GP. There is a script (which I don't know off hand) that you can run on the old server which will create the SQL commands necessary to run on the new server and create the users there with the proper ids.
Will GP V9 convertion to V10 works fine?
This question is more difficult to answer. We have upgraded without to much incident. The difficulty is in modified forms/reports and 3rd party plugins. You can export the customizations (modified forms/reports) using the customization manager on the old system, and then import on the new system - but this can fail if there are new fields or existing fields are dropped, BE CAREFUL doing this.
Backup, backup, backup - if anything goes wrong then you can restore and try again.