I've changed my spark plug last week and the engine doesn'tmove when i'm shifting the gear as what you have advice.

However,can u elaborate more on the motor/Tranny mount?

 

On my 3, there were multiple motor/transmission mounts that fasten the engine/trans to the chassis. One of them broke at 49,000 miles and it created a vibration that I could feel through the chassis (think under your butt & feet)

To see the engine shift, take it out of gear and rev it up, not real high, but get on the gas quick to torque the engine against the mounts. If one is broken, the motor would move a fair bit (say 1/2")

 

Suggest you make sureall the fluids are up to "normal operating temperatures," especially the oil, before attempting this. Drive the car @ least 5-7 miles (~10-15km.)
It's not good to free-rev a cold engine.