If I build a game that runs on a Windows phone, does that mean it will work on Android (and future ios) with .NET core or vNext? I do not wish to use XNA or C++.
Yes,it will. Microsoft is open-sourcing it, and making it available on different platforms.
MICROSOFT OPEN SOURCES .NET, SAYING IT WILL RUN ON LINUX AND MAC
SATYA NADELLA’S RAPID reinvention of Microsoft continues.
In yet another bid to make up lost ground in the long march to the future of computing, Microsoft is now open sourcing the very foundation of .NET—the software that millions of developers use to build and operate websites and other large online applications—and it says this free code will eventually run not only on computer servers that use its own Windows operating system, but also atop machines equipped with Linux or Apple’s Mac OS, Microsoft’s two main operating system rivals.
Hope this helps (=
Yes is the answer, and Xamarin is a useful to create native apps for all three major OS platforms, you could install Xamarin for Visual Studio