They are not complete sentences, because they don't have a subject and a verb. Because they are not complete sentences, asking whether they're "grammatically correct" is sort of a question without an answer. They don't contain any glaring errors and are correct as phrases. (Technically, something like "What a great shot!" is an exclamation, which is not quite a complete sentence either.)
If we look at them as stand-alone utterances, the question is whether they are understandable and idiomatic. To this northeastern US English speaker, yes, they are understandable and at least reasonably idiomatic. They are an example of conversational deletion of "That is such a bad idea/great question/etc.)" just like "What a great idea!" can be considered short for "What a great idea that is!"
"Such a warm feeling reading this post!" could be read as conversational deletion for "I have such a warm feeling reading this post!" but it feels much less idiomatic, because the deleted part in exclamations is almost always "This/that/those is/was/are/were".