If I have a texture, is it then possible to generate a normal-map for this texture, so it can be used for bump-mapping?
Or how are normal maps usually made?
I don't think normal maps are generated from a texture. they are generated from a model.
just as texturing allows you to define complex colour detail with minimal polys (as opposed to just using millions of ploys and just vertex colours to define the colour on your mesh)
A normal map allows you to define complex normal detail with minimal polys.
I believe normal maps are usually generated from a higher res mesh, and then is used with a low res mesh.
I'm sure 3D tools, such as 3ds max or maya, as well as more specific tools will do this for you. unlike textures, I don't think they are usually done by hand.
but they are generated from the mesh, not the texture.