There are many Entry level Diesel sedans in the market, which come in your budget includung Maruti Suzuki Swift Dzire, Honda Amaze, Chevrolet Sail, Tata Manza, Toyota Etios etc. All these are affordable and have good drivability, But the first two are best in class. 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.