Hi Matthias,
I don't know anything about the emulator but the demo site is working correctly on my iphone.
For testing without a phone I use a Firefox browser extension called User Agent Switcher which allows me to make Firefox pass the same user agent string as iphone to trigger use of the mobile skin, then I just adjust the window size of the browser.
Note that Mobile Kit only officially support iphone, android phone, windows phone so if you use an emulator use one that emulates one of those devices. Blackberry though not officially supported is reported to work ok by others.
Best,
Joe