"whose need of stories is matched only by the need adults have of children to tell stories to, of receptacles for their stock of fairy-tales, of listening ears on which to unload those most unbelievable yet haunting of fairy-tales, their own lives"
- Does the sentence "of listening ears on which to unload those most unbelievable yet haunting of fairy-tales" mean "The adult have the need to unload those most unbelievable yet haunting of fairy-tales on the listening ears"?
Yes, except we say that "the adults have" or "the adult (singular) has".
- Does the word "yet" mean "used for emphasizing that someone or something is even bigger, better, worse, more etc than someone or something else" in the sentence "of listening ears on which to unload those most unbelievable yet haunting of fairy-tales"?
yet means but here.
- Is the word "haunting" an adjective in the sentence "of listening ears on which to unload those most unbelievable yet haunting of fairy-tales"?
yes
- Does the word "haunting" mean "sad or beautiful in a way that is difficult to forget" in the sentence "of listening ears on which to unload those most unbelievable yet haunting of fairy-tales"?
yes
- Does the word "of" in "haunting of fairy-tales" have the same meaning as the word "of" in the sentence "It is very nice of you to say that"?
The phrase is "the most haunting of fairy-tales" and it means that it is the most haunting fairy tale. The meaning of "of" is similar to "belonging to" in this context, and it can be seen as a contraction of "The most haunting tale from the set of all fairy tales".
- Does the word "of" in "haunting of fairy-tales" mean "used to indicate that someone has behaved in a specified way"?
No, it means what I said in question 5