Xamarin doesn't provide its products on Linux. But it doesn't mean MonoDevelop doesn't work there. The latest versions run on it, it's just a matter that we don't have the manpower to keep up with packaging.

On GTK+ 2, it's still the main toolkit used by the IDE, but on windows/mac some bits of the native toolkits are used to improve the user experience.

QT on iOS and Android means you get non-native UIX. So why bother with C++?

Disclaimer: I work for Xamarin.