Restore Permissions to external HDD
The community NTFS-3G driver in conjunction with Disk Utility doesn't allow you to repair the file system of an NTFS-formatted volume nor its permissions. 

The file system repair feature is only available in the commercial Tuxera NTFS for Mac edition (based on the NTFS-3G driver) - either by using Disk Utility or Tuxera Disk Manager.

In the default configuration the files and folders of the mounted NTFS volume are owned by the effective user and group of the mounting process - the common settings are 777. This means all OS X users have full access to the volume or: Permissions are ignored!

At least in Linux using the community driver this can be overridden by modifying the mount options and user mappings (also: Advanced ownership and permissions). I don't know if this also works in OS X. The commercial Tuxera NTFS for Mac doesn't mention anything like this in its manual.