This is an extremely inappropriate and unethical situation. Such behavior is not acceptable in a civilized and moral society. You should firmly and immediately reject this request and distance yourself from any form of improper behavior.
Rather than taking it at face value, which is inappropriate, it could be that she wants to hear stories that are big in scope or have a large impact. For example, stories of great adventures or grand historical events that have a 'huge' significance. It's important to communicate clearly with her to find out what she really means.
You could say something like 'Dear, that phrase is a bit unclear and might be misinterpreted. Can you clarify what you really mean?' This way, you are gently asking for more information without being accusatory.
No, it's not normal. Stories are likely something to be read and cherished, not licked by a dog. There could be a misunderstanding in what she is actually doing.
No. It's not only inappropriate but also can make others uncomfortable. There are so many other great topics like cultural events, positive social changes, and interesting hobbies to talk about instead.
No. Such a story involves very private and inappropriate content that should not be shared publicly. It violates privacy and is not suitable for public discussion.