Could you please zip a directory (/var/vmail/..) of a newly created mailbox before and after the first email?

Hi, this bug has been fixed few days ago in ajenti-v-mail package, could you please check if you're on the latest version?

Each website receives its own FTP username and password, restricted to the root directory of the website. 

You need to enter your MySQL root password, not system root password.

The include directive is probably isn't needed here because Ajenti V adds it automatically for all PHP entries. I've posted your config as a KB article here: http://support.ajenti.org/topic/476525-/

Just create a separate website and use full subdomain.domain.com as your domain name.

If you use a desktop Ubuntu setup, you will only see lo because NetworkManager manages all others. If you use a server ISO or set up other interfaces in /etc/network/interfaces, they will be manageable from Ajenti. 

It's possible by adding a Custom Configuration code to your content entries. Example: http://stackoverflow.com/questions/19975218/remove-php-from-url-with-rewrite-rule