Hola. Espero te sirva mi aportación. La forma correcta sería decir. 1.-Si estas enojado no lo demuestres haciendo gestos de mal humor. 2.-No hagas caras de enojo por favor. ( yo lo diría de esa manera para que se escuche con educación. 3.- estas personas no muestra emoción alguna. 4.- por favor! no muestres ninguna emoción.

These sentences are structurally correct, but they might be used if two people understood what "the grumpy face" specifically was. A man might say to his wife, "Hey, don't give me the look!" meaning, there is a specific look she gives him that means a certain thing. So if someone says to me, "Don't give me the grumpy face" -- of course I know it's a grumpy face, but "the" meaning it's a certain grumpy face that between the two of us has an added meaning. Same thing for "stop doing your grumpy face" or "stop doing that grumpy" face. It tells me that there is a certain grumpy face (if there's more than one) that I don't like, and wish they'd stop. And for your last sentence, the better one is "Don't show any excitement" even though both are technically correct. It just sounds better.

Yes, all the sentences are natural. However, I wouldn't personally say 'Show no excitement' as it doesn't suit my style.

Both of these first sentences sound a little unnatural, depending on context. "Stop doing your grumpy face." makes me think the person has a specific grumpy face they do often. More natural to me would be "Don't make a grumpy face." and "Stop making a grumpy face." You "make" a face in English. The second one (stop) would only be appropriate to say while they're making the face, not before or after. For the second pair, both sound correct. They're both instructions. The first one is very formal. I imagine someone giving a speech when they say it.