what the square is for?

This is a checkbox, and it doesn’t come from the wpDiscuz. It may come from theme or other plugins.

Please watch this video: https://www.screencast.com/t/UmrmsaF3r3Q

It’s actually your setting. On the staging site I had the old layout for comments. I did the same procedure and there is an error. A bell should appear to the right of the square. https://postimg.cc/gallery/2CVz0zw

I created a second comment form and enabled it for posts. The other form has been disabled for posts. With the default settings the bell is back. https://postimg.cc/gallery/FL7dPPS

I did a double check by enabling all the plugins I use (One plugin I will uninstall soon so I left it deactivated. Just like when I had the problem.). https://postimg.cc/gallery/P81sg7p

And finally the last test. By removing the email as a requirement, the bell icon disappears and the square remains. https://postimg.cc/gallery/kBRHCdS

This comes from the current active theme. Firstly, try to delete all caches and check again. If it doesn’t help, you should contact theme support with the question.

The problem occurs when the Email field is not required. The bell disappears but not the square. Among other things, the shape of the square is not seen in full in any situation.

I disabled your plugin and the “theme” doesn’t add the square. Please investigate.

https://postimg.cc/gallery/qTQhcXZ