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Indeed, that is all you need for radiosity. There are two different (but equal) formulations. The first is to "radiate" or shoot light from each patch (in your case probably a face), and the other is to "gather" or receive light into each patch. If you iteratively do this enough times, you get radiosity. The first step is to figure out where light ...

On the link bellow you will find one of the most excellent explanations of radiosity: http://freespace.virgin.net/hugo.elias/radiosity/radiosity.htm It is worth reading even if you know it well. So funny :)

Actually skylight is one of the best applications. Point lights or spot lights are not the best fit for radiosity. Directional lights of area lights are just great for it (because they are not changing the complexity of render). Also read something about atmospheric scattering and its approximations to have nice sky ;).

Radiosity should work with any kind of light source; it's just a matter of how you define the first bounce. After the original light sources have been considered, all the surfaces that have been hit by light rays become light sources for the second pass, and so on. While I haven't implemented radiosity myself, I don't see why skylight/directional light ...