OK, so what you could do if you are moving to a new server is this
Restore your database on the new server
Upload a fresh set of files from your client area to the new server
Restore your conf_global.php file to the new server and edit the database details (and URL if needed) as appropriate
Upload your uploads folder
Now this assumes that you are uploading a copy of your site with no 3rd party plugins or applications. If you have 3rd party items, you could copy them from your applications folder, and copy your plugins folder. If you have any queries on those above that, you should contact the authors.
It is worth noting, the more you move over above what is absolutely needed (for example you are going to need to move your uploads), the more chance you have of moving something dodgy over with it. So if you have 3rd party items where it makes no difference if you lose the data, I would suggest uninstalling those entirely before you move, then reinstalling them from scratch on the new server.
With regard the license, if you are restoring on the same URL, then there is nothing to change. If you are doing it as a test, change the license key after you have done the move to your usual license key, but with -TESTINSTALL at the end. This will set your test key
Pleaase let us know if you have any further questions on that