The Phong model is much more computationally intensive, so it's not used for real-time 3d rendering (like games). OpenGL uses only Gouraud for this reason.
Dividing large polygons into smaller ones will provide a much more accurate lighting effect, since the same surface as before has more detail - specifically, each of the new polygons has its own normal vector that is used to better approximate light reflections and the shading model.
As for your lightmap test -
Notice how when the ball gets close to any wall, the parts of the surface outside the spotlight falloff area become very dark? The simplest way to fix that is to have a small amount of white ambient light in the room.
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