[radmuzom]

Can you write Java applications for Windows Phone 8? (without buying a third party software which allows you to do so)

[zoomerang]

Yes. Java can be compiled to native machine code via GCJ, and can expose a normal C++ Api.

Whether you'd want to do this or not is another story. C# and Xamarin would be a far better choice for a one-size-fits-all cross platform codebase.

[pjmlp]

No, but you can in C and C++.

Not only that, certain APIs are only available if you use them.