I would agree with Mr. awiqbal. Also the 5000Km limit that other members are talking about is true as well. Dont expect that honda guys will tune your car at 5k check-up. However you will certainly feel that your car is getting more responsive (or rather u'll get used to its drive style..) plus an increase in mileage.
Make a habit of checking the tyre pressure every week or so. If you plan to replace the tyres, dont go beyond 185 width. The cars mileage is very sensative to tyre size and pressure. keep it 28/30 psi. However 30/30 is doing fine for me these days. Honda has labeled 32/30 psi on the driver door but i have never tried that.
Sir that Dot display you saw is an instantaneous mileage meter. Its not that accurate but it helps you know when you are putting a heavy foot on your car during acceleration and general driving conditions. Note to the poster as well. Try keeping your gear shifts below 2700-3000 rpm. Not a rule of thumb. But general experience. Gives you a great mileage.
You can also increase your mileage by putting some high octane. I would say 3:1 for super:high octane would do fine although most recommend 2:1. Ir looks like this would increase your drive cost but i doesnt. The overhead you spend on the high octane turns out as increased mileage and you are even to some extent. How it does that it makes your car a bit more responsive at lower revs. You naturally develop the habit of shifting early. The car does'nt lag that much. Plus the rpms dont have to go higher. I believe your mileage increases that way. Atleast i experience this in mine.
For the air filter query, always use honda genuine air filter. For the new city, they come oil coated. Its not a myth or a kahani to charge more from the customer. It actually protects your engine as it prevents dirt particles from micron sizes to enter the engine and sand its walls. Honda japan recommends changing it at 15k+ kilometers but honda Pk is recommending to chnage it after 10K kms. It gets dirty earlier (by the looks) and it cannot be cleaned by regular air pressure hose. But you dont need to change it before 10K kms.
Hope it helps Pardon my long thesis.