When Exporting from Magento, does is remain on the website or is it removed when I export?
By default the Dataflow profiles are configured to export to the var/export directory within your Magento installation. The exact location is configured in 'Profile Wizard'.
The profile can also be configured to export to an external FTP server by specifying the access credentials for such a server in the Profile Wizard tab.
Of course the original data will remain intact and on your website.