If you by chance are able to get the problem drive "mounted again" on the Mac, my suggestion is that you connect ANOTHER drive to the Mac right away, and try to copy anything you can from the problem drive.
Even if the data sectors on the drive are ok, it sounds like there are directory problems.
What I would do in your situtation:
1. Get another drive (or, get a "bare" drive and a USB3/SATA docking station, go to amazon and enter "usb3 sata dock" into the search box)
2. Try to get the problem drive mounted, and copy all the files to the second drive
3. RE-initialize the problem drive with Disk Utility and test it by running "repair disk" on it a few times
4. If it looked ok and passed all the tests, then I'd re-copy data back to it. But I'd ALSO keep copies of the most important data (the stuff I absolutely didn't want to lose) on another drive, as well.