Spherical Environment Mapping?

I don't think you need to add anything special, just enable texture coordinate generation for sphere mapping.

As long as the normals of your model are correct, there shouldn't be any problems.

I am wondering this too. Do you basically render to a cubemap around the sphere, and then perhaps in a shader calculate a reflection vector to lookup the texel to use from the cubemap?

These coordinate generators are designed to work with cubemaps; the range of the coordinate vectors are -1...+1. However, you could apply a texture coordinate transform that scales them to 0...1 - which is the range for a 2d texture - effectively stretching the texture to cover the mesh.

The transformation needed is a simple combination of scaling and translation of the x and y vectors (or u and v in the context of texture coordinates). You don't need to modify z since it doesn't get used with a 2d texture.

I recommend using the camera-space reflection as the generator for "chrome" coordinates, it is the most physically correct one out of the options, provided that the texture image is defined spherical coordinates.

EDIT: I assume that D3DTSS_TCI_SPHEREMAP would convert the flat texture space into a spherical one automatically. Haven't tried it, though!