it almost sound like the problem may lie inside the headlight switch on the side of the steering collum. With something like this, its almost a "hit-and-miss" situation to fix the problem... you have to start eliminating potential problems. One of the easiest, check all the fuses first... your car has 4 fuses for the headlights alone, one for each bulb basically. The DRL system works seperate from those fuses, on its own circuit, also seperate from the headlight and high beam switches inside the car.

With the brake light, is it the same one that comes on when the parking brake is pulled up? Or the little indicator that lights if there is a brake lamp out? If its the parking brake indicator, check your brake fluid, if it gets low it will trigger that light. If its the light for an out brake light, there may be a loose bulb in one of the tail lights (including the third brake light in the rear window or spoiler if equipped) or the connection to the circuit that controls that little light may be loose, which is a small brown box mounted to the inside of the left, outer tail light.