Daytime headlights wont go off

run an auxiliary ground wire to verify, you might be surprised...

they should turn off when the main headlights are turned on, if not then you could have wiring problems,

No, I believe those are the marker lights

The problem with HID lights is that they require 12 volts or more to work. Daytime running lights on require 6-9 volts from the module. So when the original lights are replaced, the daytime running lights will not supply enough voltage to the HID ballasts to turn them on. The result? No Daytime Running lights. Another alternative is to purchase LED strips and place them around your headlights with a fused accessory power from the ignition switch. When the car is on the strips light up and you have Daytime Running Lights!

The blinking light is telling you that you have a headlight out, if you look the service light should be coming on when the light stops blinking.
Replace the head light and all should be fine.

Sounds like you have a problem in your headlight switch. As far as them staying on sometimes when you shut the car off are you referring to daytime running lamps or the regular headlights? If it's daytime running lamps that like to stay on and your headlights do not like to turn on then there could be a combination of headlight switch and daytime running lamp relay.

It is possible the relay gets the signal from the headlight switch as well, since they generally turn off when you turn your headlights on.

its the multi function switch at the steering column ,it is your directional and light switch combined

Check the fusible links under the hood. Also, double check the bulbs are in fact good. Lastly it could be a defective daytime running light relay.

The DRL light stands for Daytime Running Lights.
It will not hurt anything by driving the car.
I am not sure that it is even broken, does it go off when you turn the lights on?

Dash lights were falsing ? I assume you mean pulsing .
driving lights come on ? daytime running lights or park lamps ,does the vehicle have daytime running lamps . Daytime running lamps module .
Daytime Running Lamps (DRL) Module (Headlamp Auto Control Module)
Mounted behind the radio and the HVAC control, left of the instrument panel compartment.