Hi JC. I'm Greg, an installation specialist, 10 year Windows MVP, and Volunteer Moderator. If you will work with me I will be here to help until the issue is resolved.
There is nothing about deleting files using the Uninstall button in Apps Settings that could cause your files to be deleted.
When files disappear from the desktop they can often be found on the C:\User\Public\Desktop folder. Sometimes that can become hidden so to unhide the Public folders go there and choose View tab, tick the box to Show Hidden Files.
Otherwise I have no idea why. If it had been a Version Update you could look in C:\Windows.old. They may have gotten misfiled which could explain why they were found by the paid recovery app. It's always best to do copious searches for missing file names and key words in the Search box as one will show up if they are there at all, so you can right click to Show File Location.
Your files should always be backed up because a hard drive can die at any time without notice. Some suggestions to help ease into this habit:
- You can sync your Desktop, Documents and Pictures folder using OneDrive Backup, or just drag valuable files into OneDrive folder, offering 5gb free with additional space for cheap: https://www.tenforums.com/tutorials/116029-turn...
- Google Drive has a new Backup that allows you to choose User folders (Documents, Pictures, etc.) to sync up to 15gb for free to their cloud in real time so it always has the latest version. https://www.google.com/intl/en-GB_ALL/drive/dow...
- In addition I'd have an on-site hard copy backup. The best way to do this is to sort all of your files into their User folders and then drag or copy them to another hard drive, USB external or flash drive. Here's how to drag, copy or move large groups of files: https://www.pcworld.com/article/2086566/the-man...
- Besides your files you should save a System Image back up to use in place of reinstall in 20 minutes. The best free alternative is Macrium: http://www.howtogeek.com/howto/7363/macrium-ref... You can even use the Macrium program to mount and extract files from this image so it can serve as both image and file backup too.
I hope this helps. Feel free to ask back any questions and let us know how it goes. I will keep working with you until it's resolved.
______________________________________________
Standard Disclaimer: There are links to non-Microsoft websites. The pages appear to be providing accurate, safe information. Watch out for ads on the sites that may advertise products frequently classified as a PUP (Potentially Unwanted Products). Thoroughly research any product advertised on the sites before you decide to download and install it.