But very cold entities - almost not moving. The latest 'atomic' clock uses "spin-polarized, ultracold atomic ytterbium". Its not the particle motion per se that's being measured; its fields around the particle, right? Not at all relative motion.
Aren't these fields thought to be even smaller particles? Like the hypothetical graviton. So everything could be made of particles, even forces like gravity.
Yes, these electronic transitions are a form of motion, too. Change is not limited to mechanics.
Sure; but to define time as motion, and motion as time, is circular and not very useful. It doesn't explain anything.