Is there a way in Xamarin - by design - to remove unused code, a bit like Analysis in VS, or Resharper?
Well unfortunately no, at least not yet. Xamarin studio has some code styling options like Resharper, which are more extensive than VS's built in IntelliSense but that is where it ends. The tool is getting major overhauls periodically so I assume we can expect more capabilities with every major release.