A family of Microsoft relational database management systems designed for ease of use.
Tal,
Its not the Windows version that's important as much as the Project version. The latest Project 2016 version is WInproj.exe 16.0.4690.1000. If that's not what you have, run Windows Update.
Based on the problem you have and your description of the file histories I'd say the files are corrupt. One of the most used (and effective) ways to clear corruption is saving to XML however that's obviously not working in this case. I have no idea why saving to XML would cause Project to crash but here is what I suggest. Take a look at the following Wiki article and use methods 1 and 3.
Hope this helps.
John