The shaking of the head is typical to a runny nose. Take a close look at them, and listen to their breathing when they are on the roost tonight. If you hear a rattle, it is CRD. Either way, it sounds like you have a respiratory problem going on. You can see more info on this on my site HERE .
Not in my experience. What you can do is rub a little vicks vapor rub on their beaks, and wattles so the vapors help clean them out. Some birds can recover without treatment, but if it is CRD, it is much better to treat them, and yes, this can cause death, and some birds can't be relieved of symptoms, even with meds. I have found that it is best to just bite the bullet, and treat them in the long run. I understand if you don't want to medicate, that is your decision, but if they got the rattle, you may loose them if you don't medicate.