No, it doesn't. Remember that the mass of a particle is just an average: energy and time are linked by the uncertainty principle as position and momentum are, thus decaying particles (pretty much all of them) do not have a sharply defined mass.
No. For example the weak force is created by the very heavy W and Z bosons.
The uncertainty principle says you can "fudge" the energy if your time-scale is short enough, and this is what happens. A result of this is that the distance the weak force can operate over is limited, since the timescale has to be short, so the particles don't have the time to travel very far.
doesn't the energy need to be at least the mass of the virtual particle?