Support

I guess that you have set up your sudomains wrong. Namely, your WordPress site is in public_html and all subdomains are a folder of public_html (instead of a directory one level above, next to public_html). In this case Akeeba Backup correctly backs everything up: it's backup software, it's supposed to backup every directory it sees unless you tell it otherwise.

And here lies the solution to your problem. You can use the Files and Directories Exclusion to exclude the folders where your subdomains live (the leftmost icon next to these folders in the folder list). This way the backup will not include the sudomains' root folders.

That's complete unrelated and it's not even a problem. It tells you that these files cannot be read because of permissions issues. That's because these files are copies you have made and uploaded by FTP. For more information about ownership, users, groups and permissions please consult the Security Information chapter of our documentation. It's a long read but you MUST know how this works if you're running a site.