You have mentioned two best sedans of the segment and both of them comes in almost same price range. Honda Amaze has a 1.5L, i-DTEC engine which gives a maximum power of 98.6bhp. Maruti Swift Dzire has a 1.3L, DDiS engine with a maximum power of 74bhp. Maintenance cost of Amaze is higher and almost double than that of the Dzire. Maruti has India's largest service network and the price of genuine parts are also lower than the Honda. If you have to drive your vehicle in city and the running is 70-80 kms per day then we recommend you to go with Dzire. But if you want a powerful car with more attractive interiors and exteriors, and you can afford a higher maintenance cost, then you can go with the Amaze. To see a detailed comparison of these 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.