HC automatically sends mails in standard format from the panel and does not provide any interface from where you can send mail to your customers. If you are sending mails through your mail server web interface then you should contact with your concerned support.
About second question, currently the only solution can be to customize the template that you can maintain himself. The template is inc_iisfunctions.asp located at this path \Program Files\Advanced Communications\Hosting Controller\web\admin\Common of your server where you would find the replace statements.
You can make a new TAG in the mail template instead of DOMAIN_NAME
and replace it in the above mentioned file inc_iisfunctions.asp with just the domain name.
SourceFile = Replace (SourceFile,DOMAIIN_NAME," http://"
this is a line from the existing file..
You can add another line after it where ever you find it in this file.
SourceFile = Replace (SourceFile,DOMAIN_NAME_EX, NewSiteName)
where DOMAIN_NAME_EX is your tag
and NewSiteName without http:// will be replaced