Time Capsule on Public Network
To answer your first question, you hold control and option together and then double click on the Time Capsule in Airport Utility. On the summary page you will see a bunch of stuff, but under where it says "Version: XXXXX" you will see that it shows MAC addresses for all of the interfaces 

Secondly, the TC by default restricts backups to only computers that have the password which can be set under the disk tab


I don't really understand your third question, but if it means what I think it does, you should connect over the LAN port because while using the internet jack does work, I found it causes instability within the network.