Yes, you should be able to run some WINCE.NET programs using it. Remember that Portable.NET is not complete yet but it is getting there.
There is Qt support available but I haven't compiled it. It can be obtained from: http://qtcsharp.sourceforge.net/
Yes, this code should be able to be compiled for the standard ROM. I compiled it using 'with-x' to get the graphics support and System.Windows.Forms support. I don't think you'll get this with the standard ROM as they require X. You would be able to use QtSharp directly though.
I compiled everything natively on the Zaurus so as long as the 5600 can do this also then the code from the Portable.NET CVS should 'just work'. I needed to make no changes to the CVS code at all to get things to work.