Thanks for your quick responses.
thehen, you are right. Wikipedia states that openfeint was shut down ("On November 16, 2012, GREE announced that it would be discontinuing the service on December 14, 2012, primarily in favor of its own similar platform." ~ en.wikipedia.org/wiki/OpenFeint)
I'll do some research on phonegap and CocoonJS, too. As far as I understand your answers, there is currently no way to integrate Game Center.
—: So, integrating openfeint/GREE might be possible via phonegap!? How do you access those features? There is no "phonegap"-object to add, is it?