[AJT1961]

I'm not an expert, but this is what I would do first:

(1) (a) check the fuses (b) pry out the switch and make sure none of the plug connections are corroded.

(2) (a) make sure you don't have the dimmer turned all the way down, (b) check the appropriate fuses as per your owners manual diagram (c) check the bulbs.

(3) Assuming you are not just referring to the daytime running lights, and the actual headlights are on in daytime, try cleaning the light sensor on the top of the dash with a Q-tip and some windex

(4) That is normal -- the radio should go off by itself after about 5 or 10 minutes if you are still sitting in the car, or the instant you open the door to get out.