Girlfriend, a discussion.
If you are thinking of fun questions to ask your girlfriend, you should ask her in a natural way. You have to be creative, and talk about such things which sincerely display her qualities. Women like to talk and want others to listen them. Ask about her, what she likes or dislikes, her childhood memories, her fears, her passion, her embarrassing experiences of life etc. When she talks, be a part of the conversation by asking random questions to make her feel that you are interested in her thoughts and feelings.