Is the opening in the upper palate inside the mouth considered part of the throat? Does cleaning the nose by inhaling water that enters the mouth invalidate the fast? Does this entail making up the fast (qada') or offering expiation (kaffarah)?

If water does not reach your throat, your fast is valid. Even if it reaches it, and you did not intend to swallow it, the fast is not invalidated, because the criterion for breaking the fast is the reaching of the 'muftir' (that which breaks the fast) to the stomach, and its reaching the throat is a presumption of that. As for phlegm, it is sufficient for you to spit it out if it reaches your mouth, and the fast is not invalidated by that. It is advised to avoid actions that may cause difficulty.