Are GDI, GDI+ and OpenGL really obsolete/deprecated?
This is not true for OpenGL. OpenGL 4 allows you to use geometry shaders on winxp. Which isn't possible with DirectX (DirectX 10 and up isn't supported on WInXP). It is also one of the only cross-platform 3D APIs out there.
From a business point of view MS is interested in promoting DirectX since it is their technology that lock Developer into windows platform (they're also interested in making DirectX more attractive for developer, but that's another story). So it makes sense that they aren't keen on promoting OpenGL.
What else should be used?
I'd advise to stop using platform-specific tecnologies when possible. Grab cross-platform framework and use it for your application. There's Qt, GTK, wxWidgets and other toolkits for GUI apps, and SDL(and alternatives) for games. This way when platform developer decide to make ridiculous decision (like not supporting DX10 on WinXP) you dislike, you'll be able to move elsewhere with minimum development cost. Qt is also ridiculously powerful and at the moment I have no reason to use something else for GUI development. Still, situation can change in the future.
In short, while developing for certain platform you should keep in mind that platform developer might have their goals that are not compatible with your wishes. Discovering that your source has become locked into single platform isn't very pleasant experience. Your own goals should be the first priority, and if os developer tries to make you use certain technology you don't like, then you shouldn't support that technology.