MacOS – Recover the lost data

You'll want to decide to use a Mac based program like Data Rescue which offers a free preview to see if your data is retrievable:

• What should I do after I lost my MacBook data?
• Recovering files from Time Machine backup disk after wrong dd
• Accidently formated my external 1TB hard drive!

Alternatively, you could take the external drive and connect it to Windows based software and use that OS and tool to try to effect a recovery:

• I may have used Disk Utility to erase my drive - is there hope?

Worst case, you can seek professional help from various services, but since you asked for free that will limit severely the quality of the software as well as potentially the experience of the assistance available to you.

If you know the exact dd command, that will inform you as to how much of the NTFS data was overwritten and whether or not some tools will be better suited to help recover files from the unwritten portion of the drive. I would say you might have better luck with tools designed for NTFS as opposed to the Mac software as the erasing OS has less to do with recovery than the OS that created the files and filesystem in the first place.

You can't recover data directly - in the sense of recovering data lost by accidentally deleting files or formatting a volume - in Internet Recovery Mode/Recovery Mode because no appropriate tools are available in the Base OS X system.

You may clone a disk or volume with dd to an external drive and check the data on a second Mac using a recovery app like Data Rescue/Disk Warrior or Lazesoft Mac Data though. IIRC some of the apps even allow you to create a recovery DVD/thumb drive and by booting from this modified recovery OS X you may check your Mac's disk directly.