Try keeping a straight face and bringing your eyebrows down some in the middle. Not blinking adds to the effect.
If you want to give some one a cold stare, gaze at them without expression, look past them, through them without haste and hold your gaze at them. Think to yourself as you give the cold stare that you don't care what they think of you.
No, the cold and the flu are two different kinds of viruses. Usually people only have one kind of virus infection at a time, but it is possible that if your immune system has been busy fighting one...