Both sentences are unnatural. You need to add a 'so' in both cases: "Don't make so much noise while you eat." "Don't make so much noise while you are eating." I disagree with Antony in that both sentences are ok to talk about what is happening now, in the present. There is a slight difference in nuance between the two, though. Because you are using the present continuous tense in the 2nd, the listener has more an image in his mind of the on-going nature of 'eating'. The first sentence pays less attention to this sense of duration of time.

Yes, but they are not interchangeable. I would add a "so" between make and much. The second would be used if someone is eating right now, and you say "don't make so much noise while you are eating"