Another way could be 'She is interested in my story'. It focuses on the story aspect without any inappropriate or vulgar connotations, making it suitable for all kinds of friendly or professional conversations.
This is a rather strange and inappropriate statement. Maybe in a very unorthodox sense, she could be implying that his tales are so outlandish that they are 'big' in the sense of being hard to believe. However, this is all speculation because the statement as it stands is not only vulgar but also very ambiguous.
He could be the type of person who is always there for his friends in tough times. He shares his money, time and emotions without hesitation. She sees all these and loves his big heart more and more.
Sharing such a story is highly unethical. It involves violating someone's privacy and can cause great harm to the people involved. It is not acceptable behavior in a civilized society.
Definitely not. Public areas are for general communication that respects all people. Subjects like this violate the norms of public decency and can make others uncomfortable.