Sure, if I want a bowl, I smoke a bowl. Sometimes my physical condition precludes the desire. Inhaling or not you are still pushing oxygen out of the blood and so, retarding the healing of any ailment. And, I don't doubt that some find certain blends to be soothing.
I prefer not to, if it's an acute problem. Sometimes it's caused by pipe smoking itself: latakia is just inimical to my throat.
I've a sinus problem too, but since that's cronic, I don't let it get in the way of my smoking. However, I try not to retrohale; alas, I end up doing so a few times, incidentally/accidentally.
Not often. Pipe smoke constricts capillaries, the little blood vessels, and slows healing, so you could be setting yourself back. Depends on how you heal. If you're young and/or especially robust, you may be able to shrug off just about any bodily complaint, but I wouldn't push your luck. Corny, but true ... listen to your body.
I will smoke my pipe over a dozen times a day, easy... but, as soon as my health is involved, like a cough or sore throat, I have no problem putting my pipe down. IMO, I would be pretty stupid to continue smoking through a weakness in health. But, as soon as I am felling better, it's back to burning...