I tried finding the information both on their website and on the Internet, but it appears that everywhere I look, a different list pops up.
Their front page says iOS, Android, Windows and Mac.
In their documentation (http://docs.xamarin.com/), only Android iOS, Mac are mentioned at the docs front-page. I'm wondering does this mean Windows has lesser priority compared to others.
On the Internet, I've found even more inconclusive information. Also, it's hard to conclude what Windows means, mobile or desktop.
I've never used the product, but would love to try it for the game that I want to create, so I have two questions:
Thanks in advance.
To update and extend Jason's answer there is now Xamarin.Forms that let us build cross-platform GUI for Android, iOS and Windows Phone. Looking at Xamarin's FormsGallery sample app I think it is fair to say that it de facto supports Windows Phone as well.
In addition to Xamarin.Forms there's always the possibility to use Xamarin.iOS, Xamarin.Android and Xamarin.Mac for platform customizations.
Xamarin.Mobile is in a preview release and supports Android, iOS and Windows Phone. It is used as an abstracted API of the native services (camera, geolocation etc).
However since you need the local SDK's installed for compilation you need a Mac computer to be able to deply for iOS. In order to compile for Windows Phone you need to use Visual Studio and the Xamarin Plugin, Xamarin Studio is not able to do this.
To conclude Xamarin supports development for
However not all of Xamarin's API's are implemented for all platforms.