Hi,
I think we didn't go in the correct direction.
The problem is apparently not about the category database structure, which looks ok in your screenshots.
The problem is that without the error message on the blank page, we're hitting in the dark.
If the website doesn't display error messages even though the error reporting of the Joomla configuration is activated, you'll have to get the error message from the PHP error log of your web server.
So please search for that fatal error message in there.
If you don't know how to access the PHP error log, you can ask your hosting company.
The error message will greatly help in understanding where the problem comes from.