Is there a comma before "and why?" at the end of a question?

If so, would I also put commas if a question ended with "why or why not?"

Ex: Are you going to bake cookies, and why, or why not?

The sentence, with or without commas or full stop, seems ungrammatical to me as there is nothing indicating what the “why” refers to. I can only see the question of punctuation occurring if quoted as reported speech, in which case the punctuation depends on the way the quoted speech was spoken — the length of any pause.

The grammatical equivalent would, in my view, be:

Are you going to bake cookies, and if so why, and (or) if not, why not?

However I imagine that in real life situations only “why?” or “why not?” would be appropriate, depending on context.