Answer 1:
E=mc2 only for things that have rest mass. The m in there isn't the physically measured mass... it's the rest mass. There you're calculating rest-mass energy. Not total energy. The total energy expression is
E = sqrt (m2*c4 + p2*c2)
where p is the canonical momentum of the particle. So if the particle has no momentum with respect to your frame (i.e. it is not moving with respect to you) then
E = sqrt (m2*c4) = mc2. If the particle has no rest mass, then all the energy is in the momentum and thus in the kinetic energy. These types of particles always move at the speed of light when in a vacuum.
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