Granted I can't see your car at the moment for obvious reasons, but:
A little shake is normal - mechanical connection between shifter, transmission, and engine. Any movement in the engine is transmitted through the driveline and thus the shifter.
If you give it a shot of gas, it's normal for the engine to slightly rock (you're suddenly applying torque to the engine, and Newton's third says every action has an equal and opposite reaction, right?). The engine rocks slightly before the engine mounts stop it. Think about how much force the mounts absorb every time you do a NLS. Some really amazing design tech.
