>>1
Don't bother with Ogre3D or other archaic open-source projects. They're horrible and are nothing at all like what game developers are using or building for modern games.
If you go the Direct3D route, don't bother with D3D9 or D3D10, go straight for Direct3D11.
If you decide to learn OpenGL first, be wary as most tutorials and articles talk about the old deprecated OpenGL 1.x and 2.x stuff. Avoid NEHE tutorials like the plague. Try to find some information regarding OpenGL 4.x or OpenGL ES 2.0, which have removed the old obsolete fixed-function pipeline and immediate mode APIs.
Technically, Direct3D11 has more features and a stream-lined state model. It supports multi-threaded command buffer construction. OpenGL 4.2 should be getting multi-threaded support later this year.
>>3,4
Enjoy your great efficiency and awesome hardware that will support your rasterizer.
He's not that far off from where things are heading. Real-time graphics is returning to custom software rasterizers running on GPU hardware using OpenCL, DirectCompute, or other GPGPU languages.
Battlefield 3 for example contains a custom software scene compositor written in DirectCompute for the PC version and Cell SPU assembly language for the PS3 version (XBox 360 has shitty forward shading, lolol) which does the deferred shading and lighting pass.
So keep that in mind OP, you probably also want to learn about GPGPU programming as well.