I’m not a native Italian speaker or teacher, but my understanding is that bene means well, buono means good. Molto just makes either one “very.” Bene/well is an adverb, they describe a verb/action: it’s going very well, you speak very well, she sang very well, va molto bene, parli molto bene, ha cantato molto bene. Buono/good is an adjective, they describe a noun: the food is very good, the teacher is very good, the books are very good, il cibo è molto buono, l’insegnante è molto buono, i libri sono molto buoni.

Yes, the context in which you employ either: - you can say a gelato (ice cream) is "molto buono" (very good), but you can't say it's "molto bene" (very good, but with a different nuance in meaning); - you can say you did something "molto bene" (in a good manner), but you can't say you did something "molto buono" (which doesn't really translate here, as this expression would not refer to a modality of performing a given action). I guess I could provide further examples, these are just off the top of my head, I hope that helped. Also, I advise to specify this would be an Italian question, and not an English one, as it's currently among those related to English language, so it would reach a lot less potential speakers that could answer your question.