It means "you must not answer this!", "don't answer this!".Eg "open your mouth about this matter and I'll punish you". "You don't dare" means "I'll do something nasty to you if you dare", to dare ="to risk doing something".

As Johnny said, 'answer' suggests there was a question previously. Without more context, I can't tell what "you don't" is referring to. I could guess, but that may not be helpful.

"that" must refer to a question that was asked before this was said. It's impossible to know what "that" is without more context.

I think it means : don't say one more word (not even an answer for "shhhh! " of any kind )