In iOS 6, you can switch on/off the \"do not disturb mode\". Is there a possibility to do that from an app? Or is there at least a way to find out if it is set?
I don't have the exact answer, but I would recommend you research the internal settings URLs that Apple has (prefs:root=) which is documented here: http://www.techwithintent.com/2011/11/force-an-ios-5-device-into-airplane-mode-with-a-single-click/
Please note - when referencing these URLs the user will be switched OUT of your app, so this is a way to access/toggle different settings, but it is not really programatic.