This may help with the sleeping part: http://www.sleepinginairports.net/eu...en_kastrup.htm

I flew out of CPH yesterday and although I didn't eat there I saw a wide variety of restaurants, from hot dog stands to more formal sit down places. Finding *something* to eat that won't break the bank shouldn't be a problem - if places are open when you're there. Not sure if Euros are accepted (they were in Copenhagen taxis) but credit cards certainly are.