You are accessing OH2 directly when going to :8080, try using https://myhost.noip.com:443 instead. 8080 should be blocked from external access and only 443 open to outside conenctions.
Your nguix setup looks correct, however by browsing to http://myhost.noip.com:8080/ you bypass nguix and are going directly to OpenHAB. You should browse to https://myhost.noip.com, which will reverse proxy you to the OpenHAB instance on 8080. In your firewall rules, ensure that you block access to port 8080 from outside.
So think of ports like telephone extensions, where you are on extension 8080 and your assistant is on 443. Normally you give your number out as 443 and your assistance filters your calls so you only get the ones that have been authenticated. In this situation you have given out 8080 and people are calling your directly without your assistant checking their details.
Back to OpenHAB, which is running on port 8080 and Nginx running on 443. When you attempt to connect to 443, it will ask you for a username and password, and if successful, will redirect you to port 8080. You are however going straight to 8080, which bypasses Nginx and accesses OpenHAB directly without authentication. In your latest post, it shows that you are trying to run Nginx on 8080, however OpenHAB is already running on 8080 and you can only have one application per port. Recommend you go back to the original configuration.
As @greg said, you should be able to port filtering on your router, which is probably the best method. You can also port filter on the Pi, just search google for your distribution and firewall. I assume you are using Raspbian so iptables is probably the recommended, though I have not used it personally.
