Yes, the authorize.net email will not contain the shipping and tax information, you should be storing the the order information in a database when the order is processed and using this for you in house records, not the email.
sending emails through Godaddy can be difficult at best, they are faily sttrict with the smtp servers.
first, you will need to make sure your hosting account with them is on a linux server. Mail on the windows servers will not work with go daddy.
you will also need to make sure your php server is configured to run php 5. mail on a php 4 server will not work.
If you are on Linux hosting with PHP 5, make sure to set the SMTP server in universal Email to smtp.secureserver.net and use port 25.
make sure to set the From address to a valid address on your domain.
