My uncle has to get tested for drugs in his job and yes- he told us about this story. He takes medication with codine in it and his test showed traces of cocaine. He showed then he was on the medication and everything was fine.
Don't worry about it- as long as you have proof you are fine.
Yes you can.
Although, if you are prescribed to the prescription meds that contain codine - all you have to do is bring your prescription or a letter from your doctor saying that you are in fact prescribed to it.
If your not prescribed to it - then that's just another illegal drug you are taking.