Please ensure that your firewall and/or antivirus are not blocking connections to the following (* indicates a wildcard selector): *.kovaaks.com *.api.gameanalytics.com *.events.gfe.nvidia.com
If you want to backup most of your files/settings go to “SteamLibrary\steamapps\common\FPSAimTrainer\FPSAimTrainer\Saved\SaveGames” and copy the files to another location.
If you want to save your KovaaK's Maps or challenge score stats, make sure to backup the folder “SteamLibrary\steamapps\common\FPSAimTrainer\FPSAimTrainer”.
Sometimes Windows doesn't like to handle refresh rates properly when games enter fullscreen in ways it doesn't expect. Try alt-enter, alt-enter, and see if that helps at all.