Yes, Honda Amaze has enough space for 3 passengers at the rear bench. Yes, Honda Amaze has the similar quality that of the Swift Dzire and it is more comfortable compared to the Swift Dzire. There are two automatic variants available. Amaze SAT and Amaze VXAT cost Rs. 6.62 lakh and Rs. 7.50 lakh respectively (Ex-showroom, Delhi).
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.