One of the most important thing a lady does is respect another person privacy. There are some things that are just to personal to ask. The list will vary depending upon the degree of emotional intmacy invovled in your realtionship, but here is a non-exaustive list of things one does not talk to mere aquantaces about
Your Health in any detail
You romantic life
Anything that might be considered drama
What does that leave you with? Quite a lot! You can talk about anything you have read new stories (without political commentary), pleasant news about people you both know, food you have enjoyed and all sort of lovely things.
This is not to say that one never talks about these things, you can do so when it is in context, for example at a doctor’s appointment to a nurse, or when you are deliberately breaching an emotional subject as a way to create intimacy. If you do breach such a subject be sure to give the other person a graceful way out. Pressuring people in to defending their boundaries and not giving them a graceful way to reject intimacy is not a kind thing to do. Of course others might choose to bring delicate subjects up.
Personal revelations are a way to build emotional intimacy and should be treated as the privilege they are and not forced. If you are known for your discretion you might find that people want to confide in you, that is lovely and you should be as gracious as possible about people wanting to share. All the same remember that listening is itself an intimacy and you need never agree to an intimacy to be polite, a simple “I am afraid I am uncomfortable, can we talk about something else” is just fine.