Mitsubishi Repair: Lights go on when they should stay off, lighting problem, winter tires

Question
Hi,

2 months ago I bought a brand new Mitsubishi Lancer 2006 (1.6 Invite). Still I have 2 issues:

1. On bad roads(cubic stones also), I have a resonance noise at about 30-40 km/h. the whole steering is just vibrating provocking much disconfort. The mechanics blame my tires, which I am going to change after the winter passes. I can not beleive that my tires are to be blamed.
Q: Do you have any idea on what can cause this resonance?

2. If all my lights are on and I stop the engine all the lights go off, which is cool. I arm my alarm, which is UNGO 100. I hit the tires until the alarm goes on. After 30 sec, the alarm will go off(which is OK, and respecting the law). The problem is that after 5-10 minutes all the lights go ON. This happened last night, and the car battery went to no power, so I could not start the car, I was late 4 hours to work, and so on.
Q: Can you point me where to look in order the lights will not come on again?

PS: The mechanics from waranty do not seem to be so well prepared. All I want is to use all the features my car has.

Thanks in advance for your response, which I hope will also be by e-mail.

Answer
Marius,
Unfortunately, I'm not very familiar with Mitusbishi models that were sold outside of the United States.  In the US, Mitsubishi uses a 2.0 litre engine in there 2006 Lancers.

But your vibrating problem can be caused by tires.  If you're using winter tires to get better traction in the snow, that can cause excess vibrations.  And depending on the style of your Lancer, its front suspension my be stiffer and sportier than in previous years.  A tighter suspension and a larger tire size will cause more vibration than normal on rough roads.

As for your lighting problem, that is probably due to your alarm not wired properly.  If that alarm was installed when you bought the car from the dealership, the dealership should be responsible for finding out the problem.  If you brought your car to an alarm install shop after you bought the car, you should take your car back there and have them verify the wiring was installed correctly.
Good luck!