You'll need to execute the respective app and pass the file as parameters.
Why stress over this if you're selling it, leave it to the prospective owner to decide what they want running.
Uninstalling WINRAR and deleting the folder followed by reinstallation would have set all the permissions as needed, it does not need to run in Win7 compatibility mode. It's folder is owned by the Administrators group.
Not if you back it all up first, make sure all your internet browsers are signed in and your history and passwords will be safe.
You could also do an InPlace upgrade that will repair your installation without losing data.
You posted the same issue with Edge browser in January, it seems to me it's time for you to do a full Windows reinstall to address this and your myriad of other issues.