When I run a profile, does it copy every file? Does it only copy new and changed files?

By default a SyncBack profile only copies new and changed files. This means when you run a profile for the first time, it will probably need to copy all the relevant the files from your source to the destination. However, on subsequent runs it will only copy files that have changed, and new files, so will be considerably faster.

With SyncBackSE/Pro you can perhaps also enable the Fast Backup option for the profile to further decrease the backup time, although this is not possible with some profile configurations (for example, not with backup from FTP). Fast Backup should only be used when no other person or process (including 'another profile' - of any kind) will be changing the contents on the Destination. This is because it works (on run-2 and later, unless/until configured to Rescan) by not scanning the Destination (thus, a Fast Backup profile will not be aware of any changes to the contents of the Destination unless it performed them itself). See the Help on the Fast Backup settings page, and also the other relevant Technical articles (a search on 'fast' should find them all).