air filter

Hello,
I've got an Accent 2003 1.3 GL, 85 bhp, euro 3.

1. Does anybody know what is the black box in front of the air filter? What is it doing? What happens if I remove it?
2. Actually, I want to replace all air filter sistem with an induction kit (K&N, Pipercross, Green ...). Anybody did this? My dealer told me that I will get "check engine" light on.
3. Did anybody tune the chip? How, where, how much and what was the result (power, torque, consumption)? Does it worth? (your opinion)

4. Consumption is realy 5.1/7.8 L/100km, but only on summer. On winter, under 0 deg. celsius, consumption rises with 25%. It is normally or it may be somethig wrong with my car ?

Thank you a lot and have a nice day ... every day.

5.1/7.8 L/100Km = 47/30 mpg
non agressive riding

I have a 2001 Accent and I have removed the first stock air box. But not permanantly.
Here's what it does:
It's a snorkel to keep water out.
It silences intake noice

-with it off, you free up some airflow, it sounds amazing! but it does suck in hot engine air.(Not a big concern to me seeing how it does run a little faster)

Take it off and give it a try, 2 screws that's it. Not tested in rain be careful though.

oh and less mileage in the winter too, no problems with your car.
I know that I get almost 200km more per tank in summer driving then winter at times.