SSL Education

I need some wisdom on understanding SSL and the "right" configuration for Exchange 2003 SP2.

My company host our website with a 3rd party vendor. Lets call website adam.org. I have an exchange 2003 server on my local area network, so the Exchange is a member of adam.local. I installed a self cert on my exchange server and its been ok, anytime you use OWA you get an error, and you can always choose to ignore and press on.

The actual cert warning is "The Security Certificate persented by this website was issued for a different website's address"

So how do I go about getting rid of that warning? Will I always get that warning with a self cert? If I was to install a new SSL cert on my exchange server does the new cert need to match the .local or the .org? does it need to match the name of the server instead of the domain? for example exchange.adam.local?

Plus any documents on how to install a 3rd party SSL on an Exchange server?

In addition, our boss wants to use a different domain name for our website, instead of adam.org they want to use eve.org but still have adam.org point to eve.org. How does this affect the SSL on the exchange if our email addresses is eve.org but our exchange is still a member of adam.local?

Any advice would be great, thanks.