I downloaded Xamarin Studio and started a trial license, created a new Xamarin forms project and clicked build (with literally 0 changes to anything, just your default download) and this is the result:
The type or namespace name 'Xamarin' could not be found (are you missing a using directive or an assembly reference?) (CS0246) (SampleFormsApp.Android)
Error CS0246: The type or namespace name 'AndroidActivity' could not be found (are you missing a using directive or an assembly reference?) (CS0246) (SampleFormsApp.Android)
Error CS0246: The type or namespace name 'Xamarin' could not be found (are you missing a using directive or an assembly reference?) (CS0246) (SampleFormsApp.Android)
Error CS0246: The type or namespace name 'Page' could not be found (are you missing a using directive or an assembly reference?) (CS0246) (SampleFormsApp.Android)
Can you release a product that functions? Thanks