Hi Gemius,
Thank you for your question.
Did you mean you install Exchange server on DC? If that. It is not recommended by Microsoft, we could refer to the following link:
https://technet.microsoft.com/en-us/library/ms.exch.setupreadiness.warninginstallexchangerolesondomaincontroller%28v=exchg.160%29.aspx
What is about Exchange infrastructure?
When Exchange 2007 and Exchange 2013 are existed, we suggest Exchange 2013 receive and send email from/to Internet.
What did you mean the same URL?
If you mean the OWA URL, we could not worry about it, because Exchange CAS server will proxy it to proper CAS server for user request.
We did not configure public IP address on DC(Exchange server). We could refer to the following link to public Exchange 2013:
http://blogs.technet.com/b/exchange/archive/2012/11/21/publishing-exchange-server-2013-using-tmg.aspx
If there are any questions regarding this issue, please be free to let me know.
Best Regard,
Jim