好不 + [two-syllable adjective]
好 + [adjective] + (啊)
好不 before a two-syllable adjective is an exclamation, "how very" or "so". The 不 in it does not negate anything: 好不热闹 and 好热闹 both mean "so lively".
好 + adjective is the everyday spoken form, often with 啊 at the end. 好不 + adjective belongs to storytelling and descriptive writing, where it sums up a scene or a feeling.
好不 takes a small set of two-syllable adjectives of mood and atmosphere: 热闹, 开心, 痛快, 伤心, 得意, 威风, 快活, 羡慕. It does not go before a one-syllable adjective.
好不容易 and 好容易 both mean "with great difficulty", so here too the two forms say the same thing. 好不容易 is the one you hear more, and it usually takes 才 before the verb.
Read 好不 as "not good" and the sentence flips. The negative of an adjective is 不 + adjective, with no 好 in front: 不热闹 is "not lively".
好不好 is a different thing: an A-not-A question, "is it good?" or "OK?". 这个菜好不好吃 asks whether the dish is tasty; 好不热闹 is an exclamation, not a question.