Email Forwarders

Email forwarders simply forward any email sent to that address to another email address. You can setup multiple forwarders to and/or from the same account.

I have found that if you send email from Gmail to an email address which forwards back to the same Gmail, then Gmail will not receive that forward. (Ours is the same way.)

How can I stop my email mailbox from keeping a copy?
You must delete the mailbox from Email Accounts, and only keep the forwarder. This way the email will still forward, but the emails will not be saved at the first address.

Can I have all the outgoing email forwarded to my email address?
No.

Is it possible to set up e-mail accounts that forward to more than one e-mail address?
Yes you can. You just need to log into your site's Control Panel and click the Forwarders icon, and then add a forwarder with the destinations separated by commas like so:
support@domain.com --> email@domain1.com,email@domain2.com,email@domain3.com