The original question was, would a packet of matter behave different when moving through space than when at rest. The answer is still "no" because the question is flawed in the first place. You cannot say that a packet of matter "moves" without giving a frame of reference. Therefore, if I travel the same speed as the packet, to me it is not moving, while a different observer might say that it is moving. The point is, the physics within the packet does not change.
Not really. Quantum physics shows that the behavior of small particles can be extremely accurately predicted by using some wave based equations. This does not say anything at all about what the particle really is. The units of quantum wave "oscillation" are "imaginary inverse square root meters." This is not even a physically meaningful unit. Any quantum mechanics instructor would berate you for attempting to assign physical meaning or reality to the wave function.Quantum physics, for instance proved that light itself sometimes behaves like a wave and sometimes like a particle.
EDIT: Light is a slightly different case, because it oscillates within physically measurable fields. Feynman, creator of modern quantum electrodynamics, fervently believed that photons are particles, they are never waves, and he imagined wave phenomenon as being explained by little tiny "clock hands" travelling with photons as they follow an infinite number of tiny paths through space time, and integrating over all paths simultaneously to predict the path of the photon. If you can get your head around that. He hated the idea that light was a wave.
The question is still open. Personally I think the answer is irrelevant, since the equations work.