I can get informations about video-files like resolution by using the Shell32.dll under windows.
Is there some way to do this (in C# - running under the mono framework) that will work on Mac?
Since the question is unclear to me, here are two part answer:
1. if you want to check the resolution of your screen (desktop):
Check if this is implemented: System.Windows.Forms.Screen.AllScreens.
For now, there is some code for it but it's marked with [MonoTODO] attribute.
AllScreens: http://msdn.microsoft.com/en-us/library/system.windows.forms.screen.allscreens.aspx
Source for the library: http://www.java2s.com/Open-Source/CSharp/2.6.4-mono-.net-core/System.Windows.Forms/System/Windows/Forms/Screen.cs.htm
2. if you want to check video file resolution
For that, I would seek ffmpeg built for Mac and using command line parameters extract resolution information from the file.