And you should PAT/NAT what is coming from "outside" in destination of the port 53 (in your case)
For the domain name take a free one for example on azote.org
And then configure it to be able to administrate your domain name...

I'd never have this problem but first you can verify that you receive packets from gmail-servers, or compare gmail's packets and hotmail packets for example...
Do you have anything related to your problem in your logs files?