I am using the comment_form plugin in Pages to have a guestbook. It works quite well, but I cannot figure out how to add data like "city", "country", etc. of the comment's author. It seems that these data are also not added to the comments database.

Thanks in advance for your help.

The comment_form plugin provides these extra fields. You can enable them on the plugin options.

But do you mean the fields or the display of the comments itself? In that case you have to create your own comment display functions based on getLatestComments/printLatestComments() /comment_form/functions.php). Those simply don't get and print these.