Be sure the cooling system is full. Feel the radiator hoses after the engine has been running 15 to 20 minutes. They should be too hot to hold onto for very long. If they are not, suspect the thermostat. If they are, feel the heater hoses. They should also be hot. If they are not, suspect a plugged heater core. They can be back-flushed with a garden hose. If they are hot, suspect a problem with the temperature door actuator or the HVAC Computer.
For the brake lights, see if the cruise control works, and if it does, will it cancel when you tap the brake pedal. Does the center high mount brake light work?