Where it says "Assessment: SELF-TEST FAILED", this is a good indication that your hard drive is failing S.M.A.R.T. tests which generally means that the drive itself will not last long and parts may already be unreadable.
Windows 7 would have been installed to an NTFS partition. Ubuntu can read and write to valid NTFS partitions without need for any additional software. If you had a valid mountable NTFS partition at this location, it would be listed as NTFS and it would be mountable.
However, what I see is that you have "Free Space".
"Free Space" existing where there should be a partition is not a common symptom of drive failure. "Free Space" means there is no partition at this location. It's likely that you mistakenly deleted this partition somehow. So this could be a separate issue from the pending hard drive failures.
Right now, since you are getting the drive failure flags, and you have suggested that you have important data on the drive but have failed to keep appropriate backups, my suggestion is that you stop using the disk immediately and take it to a professional data recovery technician
At the very least you might be able to image (copy) the disk to another disk in case this one fails.
You do have a few limited options to try to find lost data on your own, but you risk further damage to your drive if you're not careful, and the failure of S.M.A.R.T tests adds in an additional unknown factor of continued drive failures.
I will say that trying to recover files after the file system or partition has been deleted is usually not successful.
Here is some further reading if you want to go down the path of trying to recover data from a deleted partition or broken file system:
Unable to mount NTFS external hard drive
Fix corrupt NTFS partition without Windows
And in the future: Back up. Back up. Back up. Hard drives are considered "consumable". They do not last forever and most hard drives have an advertised lifespan of 3-5 years, even though they often last for longer.
