So you can't say Γιατί δεν? in case you want to say why not, right?
I really don't know for sure, but according to what I've seen, I think "δεν" only applies when it comes before a verb, like "δεν έχει..." or "δεν τρώω..."
That's right. Here you need "Γιατί όχι." "δεν" is used with a verb. "Όχι, δεν ξέρω." "No, I don't know."