I don't know much, except that it's in Dusseldorf and Youri Vamos is its director. They keep a low web profile!
I found their web site.
http://www.rheinoper.de/It's in German, but even not reading German I could guess that they do take Americans because there's a page with directions to the theater in English, and there's a notice of their (last year) auditions.
I also notice that Joyce Cuoco is their ballet mistress. She's an American dancer -- you might try writing to her. The addresses are on the web site -- click Kontakt at the top right.
Good luck! I hope some of our German posters will be able to tell you more (and you might want to ask the same thing on Ballet Talk For Dancers in the Cross Talk forum, if you haven't already)