When talking about an object moving with a certain velocity it is important to understand that from that objects frame of reference, IT ISN'T MOVING. Think about it. If you are in a car traveling down the road, you easily say that the Earth is moving underneath you. We only make the distinction that we are moving and not the Earth because it is convenient to use the Earth as a point of reference. So nothing happens inside the particle during movement.
Atomic and molecular orbits are far more complicated, but suffice it to say that the concept of an electron physically moving in an orbit around a nucleus is not correct. The electron is described by a wavefunction that has a range for its momentum and position and you cannot say that it is actually moving around. This is a very weird concept but an important one. Instead of speed, we have momentum and energy associated with the electron. An electron can gain energy which corrosponds to an increase in momentum, and thus be promoted to a higher "energy level", but again this shouldn't be associated with physical movement in an orbit. Any basic book or article on Quantum Mechanics should be able to explain all this in more detail.