Hi Julita-
Generally speaking, W3 Total Cache shouldn’t interfere with your media library or editing screens, especially once it’s been deactivated and uninstalled.
If possible, can you enable WordPress Debug Logging and let us know what the 500 error was?
There are a couple of steps you can take to make sure the uninstall process was cleanly finished.
First, delete the wp-content/cache directory and make sure that the wp-content/plugins/w3-total-cache directory was deleted when you uninstalled the plugin.
Then, check your .htaccess file for any remnants that might not have been deleted. Look for any code that starts with # BEGIN W3TC (feature) and ends with # END W3TC (feature) and remove the lines in between.