

It’s the unofficial updater for nVidia graphics on Linux. If you’re running Mint you should use the Driver Manager software instead, imo
The PPA just provides the packages, you can actually install them through the Driver Manager after adding the PPA. However, without the PPA, the newest available version seems to be 550, which is not new enough for a 50-series GPU.
Like many others here, I think the most likely explanation here is that you did not fully shut down Windows and it still holds a lock on this partition. You can force an actual shutdown in Windows by shift-clicking on the start button -> shutdown.
However, I would also recommend against sharing your Steam library between Linux and Windows. I also tried this with NTFS a few years ago and it caused me a lot of headaches. I had a lot of weird issues under Linux that went away after I finally switched to ext4.