I strongly suggest keeping the german url's on the german domain, too.
For usability and for seo purpose.
The Germans won't search for the english terms and text - so it is kind of useless, too.
If you don't have the possibility to translate your whole website and you want to add those pages where you don't have any translation put at least a GERMAN url on the page. Then you can explain in short terms that this page is only existing in english language and refer them to the english dependant - or even put in the Google translation widget (but we all know that this is not a perfect translation at all, but better than nothing).