so, as i understand there's no real problem, but you want to see your outgoing settings, right?
open the exchange console, navigate to the left side near the top, server config
then hub transport, double-click your server at the top, look at external dns lookups. this is how your server resolves where it wants to send mail to. usually it's using the dns server specified on its network card - which should be your own dns server or possibly itself.
to see that, you'd go to the admin tools on the start menu, dns
back on those properties, check out your log settings location, this will be useful for troubleshooting
back on the left, up more to the top, organization config, hub transport, send connectors, default send connector
this is what your server claims to be when sending mail - it should match your ISP provided reverse-dns entry for your outside ip address, or some servers won't receive mail from you. maximum message size is also interesting.
address-space tab there, says what this connector is responsible for. * means basically any address any domain, not covered by another higher priority send connector.
network tab - use dns mx records - this is how mail flows. everyone has an mx record for their domain, your server figures out what it is and sends your outgoing email to that mx record, hopefully they accept it.
you could have a smarthost configured here, that means just dump it all up to your ISP and let them figure it out. some isp's require this.
that's the basics - am i on the right track or were you looking for something more specific?