appengine and no-ip.org
You can't do this, because you don't own no-ip.org. In order to use a domain with App Engine, you have to set up Google Apps on the domain, and in order to do that, you must own the domain.
As mentioned in the comments, buying your own domain is your best option.
I'd like to run an appengine app on a subdomain 
like something.no-ip.org instead of something.appspot.com 
is this doable? If so, can you please help me understand? :)
Thank you so much for your help!