The classic form for a basic declarative sentence in English is: subject - verb - object (optional).
So a minimal declarative sentence is two words, like, "Alice walked."
Of course you can add all sorts of complexity: indirect objects, prepositional phrases, etc.
A basic interrogative sentence is: interrogative word - verb (or helping verb) - subject - verb (if first was helper) - object (optional). So a typical simple interrogative is, "Who is singing?" or "Why did Bob leave?"
The interrogative word can be omitted in some cases, notably when the verb is a form of "to be" or "to do". "Is this car for sale?" "Did you invite her?"
We often omit even these basic pieces from an interrogative. "Why?", "Who?", etc are very common questions. We could debate if they're complete sentences, maybe not, but they're acceptable in even the most formal writing.
"Did she go not?" is incorrect. As BlueDot says, you can say, "Did she not go?" I disagree with BlueDot that that would be "theatrical". It is more formal than most people would use in conversation, but not unheard of. But as he/she says, usually we contract this to, "Didn't she go?" Note that when you use a contraction like this, the "not" jumps over the subject so that it can join "did".