I found in emails it is best to discuss things that are personal to the girl. I had a nice long conversation about a girl I like's boyfriend. Sounds odd but it works to bring you closer. Also the best things to do with when talking to a girl though email is to firgure out the times she is online, since people usually get online at the same time every day, or close to it. Get on at that time, email her and wait for her response, IM is better but this works, then email her again, you can stay on for hours just emailing her back and forth. I can not help you with what to put in the email, but I always start it off with a question. If you know the girl ok and you want to know if she has a BF, and you know one of her ex BF's names then just ask her if she has a BF. She will usually tell you, the truth the most of the time, and then ask you why you asked. if you do not want to tell her the truth, then say something like oh, one of your ex's wanted me to ask you. Then she might ask you who it was, and you are prepared, but to make you closer with this girl you might try playing a quessing game, just little things to make her more attracted to you.