Honda Amaze diesel version accelerates in 2nd, 3rd gear even without touching accelerator. In city traffic, when you need to move slow, every time you have to apply clutch and brake to keep the speed under control Further when you need to slow down, you have to bring gear to neutral else the car does not slow down.
Is it possible to adjust the Idle speed of the engine.
These are two different scenario's that you have pointed out. It appears that you are getting confused with engine braking, because when you leave your car in idle on the move it starts to de accelarate it self, on a wide clear road the phenomenon is pretty evident, but when you do the same in traffic it doesn't appear as the short distance don't allows it to de accelarate as expected. So, it is just matter of getting used to your new car, there is nothing wrong with it and we won't suggest you to bring gear to neutral while on move as it directly affects the mileage of your car.
The engine noise is coming in the cabin because of poor cabin insulation and it depends on various things like gaps between panels and doors, material quality, etc. You need to get major changes in the interior for better insulation and we won't recommend that.
You should go for the fourth servicing despite the fact that you have not driven your car much. It is important that you go for regular servicing. Whether you want to go for wheel balancing should depend on if your car is bobbing while driving or it is not going in straight line.
The choice of the variant between diesel and petrol would depend on what would be your monthly run. If your monthly run is more than 1500 kms, you should go for the diesel variant else you should go for the petrol variant.