Clearly you are new to automatics! You don't need to put the car in neutral at traffics lights etc, just keep your foot on the brake or hold on the handbrake, I would only ever put it in neutral if I had a long wait ie train crossings etc.
The vibration at low speed could be a transmission issue but very difficult to diagnose via the forum as it could be a number of other things...
The rev changes are normal, and given you have a UK car it has the cold weather vents in front of the radiator to help when the engine is cold.
Outside of all of these it is a great car and just enjoy!!
Always said I would go back to a 6 series