How do I disable the subject? In Drupal 8 I visited admin/structure/comment/manage/comment/form-display and disabled the subject.

1- The subject field is gone, but the subject label for comments is still shown. Is there any option to hide that, or should I change the theme?

2- It looks like there used to be an Allow comment title setting for each content type. Has it been removed in Drupal 8, or is it just me who cannot find it?

3- How can I avoid an empty comment title is automatically filled with the first words taken from the comment?
I find the Automatic Entity Label module to do that.
After making a backup of your Drupal database and folders, require it with composer and enable it.
Now you will see a new 'Automatic label' tab in the comment type management, and by clicking 'Automatically generate the label and hide the label field' you will be able to use tokens to auto fill it.