Re: speed of light...
One suspects you mean classical force fields.
For a classical field you only have light and gravity, and these propagate at c. But if you include quantum theory fields it all gets vastly messier.
The weak force is mediated by the W and Z boson. These have mass. The strrong force is mediated by mesons, and they have mass, although the residual strong force is arguably more to the point and mediated by the massless gluon.
A field is just some property you measure in 3D space. Pressure is a perfectly good field. Albeit not one that measures one of the fundamental forces. It propagates at the speed of sound. You can have a perfectly good quantum field theory for sound. The sound particles are phonons, and they mediate the pressure field, and travel at the speed of sound in the material - which need not be isotropic.