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-
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There is no official communication for the new version/facelift of Honda Amaze as of now.
Talking about the current Amaze facelift, it was introduced last year and is priced between Rs 5.60 - 8.53 lakhs (Ex-showroom, New Delhi). The car has a new front/rear bumper, reworked radiator grille and new taillights on outside and a new dual-theme dashboard with an automatic climate control system inside. Engine wise, it retains the same 1.2-litre i-VTEC petrol and the 1.5-litre i-DTEC diesel engines.
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.