Attempting to retrieve files off hard drive via terminal

I have a 2011 Macbook Pro running Mavericks. Recently it froze and upon restarting I was met with the dreaded circle with a line through it. Here is what I've tried:

The Macintosh HD is greyed out or ghosted so there is no booting from there. It appears the partition is missing. Unable in recovery mode to reinstall the OS via internet recovery nor (yes, I know…learned the hard way to not put off backing up) backup. I have taken it to Apple Genius bar and the hard drive is fine.I'm trying to recover any photos, documents, etc off the drive and Apple attempted to retrieve via their OS as well as Target Disk Mode which also was unsuccessful. Apple's advice was to wipe clean and reinstall the OS losing everything or trying an outside vendor that may be able to retrieve files. My understanding that is rather costly hence my desperate attempt at doing this myself. I thought I could run a program such as DiskDrill etc from external drive but don't know how to access/run programs off the external drive via terminal?

I'm attempting through terminal to retrieve manually any folders possible. I am not code literate yet can follow instructions well. I've been relying on code I've picked up on other Apple forum threads. I am unable to even find the main folders expected i.e. Documents, Pictures, Applications etc. My understanding is upon typing in cd / and ls that I should see all the folders which I'm not. I've attached a picture of the screen as I have no way of copying and pasting the results.

ANY suggestions or exact coding would be appreciated. I'm not even sure at this point this is feasible. Thanks in advance.