The first question is easy, go to Preferences, General Prefs, Security - see this picture and click the bottom option. Like it says in the box you'll still need to add email address to the book to get the to auto appear.
The second question... are you accessing the Exchange server via POP3 or IMAP/Exchange? I use an Exchange server for work and can send emails anywhere in the world. does your school allow external access? have you put the OWA address in the server box when you setup the account? what version is your Entourage, Mine's 11.3.3
To go the other route via Gmail, I think you'll have to first setup Gmail to spoof your Exchange account. Log into Gmail, then go to Settings and Accounts, add your Exchange email address - you should now be able to send that email via Gmail's server
if you haven't already setup your Gmail account in Entourage, here's how.