If you do not intend to completely lose the chance to continue the relationship, forget about the questions about her former partners. At the same time, in conversations about these topics should be taboo.
A very safe topic of conversation is the topic of her brothers and sisters. About the parents prefer not to ask. You may not know, perhaps this issue will cause her depressing memories. In contrast, brothers and sisters, usually associated with positive emotions and also you probably will show interest about her family.
Want to charm? Ask about beautiful places she visited on the last vacation or where she would like to visit in the future. Thus, you will give her the opportunity to talk about her dreams and, in addition, will be able to determine whether you have common goals and experience.
Food and drinks
Although this well-known theme is something of a cliché, but still works reliably. During lunch/dinner in the restaurant is more than natural to ask, what food and drink she loves. In addition, if you find that prefer similar dishes, you will have another topic of conversation. A bonus is the fact that it is a completely safe topic that can not go "something is wrong".
Ask her what University she attended, why did you choose this field, what kind of people met or lived in the dorms... the Theme of education is virtually inexhaustible. In addition, you can create a warm atmosphere and offer stories from his student years.