Honda Amaze gives a city mileage around 21kmpl while the mileage on the highway is 25.8kmpl. Maruti Suzuki Swift Dzire gives 23.4kmpl on highways while 18.6kmpl in cities. Swift has a 1.3L DDiS, 74bhp engine while Amaze has a more powerful 1.5L i-DTEC, 98.6bhp engine. The maintenance cost of Dzire and Amaze are alike, a little here and there can always be there. Maruti has widest service network in India and spare parts costs you pretty cheap. So both the Dzire and Amaze have their goods and bads, you can buy any of these two. To see a detailed comparison of both the cars, please visit the link below-
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.