I'm not as pessimistic about OnlineGirl as other people,... on the contrary, I see plenty of good points. My suggested answer would go along these lines:
"I'm very sorry I hurt you, and I understand why you sent your first mail. That's also why I appreciate very much your second mail, which shows that you have the ability to cool off, and reach for the other person. That's important for a long term relationship.
I'm trying to be honest with you, and I think we should clear some things off: I'm not dating anyone, and this includes you. I can't see myself dating you before I even meet you. I am very interested in getting to know you better, and am not passing on you. But for that, we really need to meet. Since this is not possible for the moment, you and me will have to accept that things will take time.
Also, although I wish to date a girl (and only one girl), past experience as thought me that it's best to proceed cautiously, and really get to know each other, before deciding on whether we should date, or have a long term relationship. I think that you will agree with me. This does not mean I am rejecting you. I am giving a chance for an healthy relationship to develop between us.
Finally, I do not wish to be your friend, I am in contact with you because I want to date you. If it turns out that this is impossible, then we may wonder whether a friendship is possible. But for now, that's not what I'm interested in.
To finish, I would like to apologize for mentioning that I chat with other girls. Although it's unpleasant for you, it was uncomfortable for me not to mention it, since I had the impression I was lying to you by omission. The point is that at this moment I do not consider I am dating you, so I don't forbid myself from getting to know other girls. Obviously, I also can't ask you not to meet other people. However, I think you should keep two points in mind: 1. I am spending quite a bit of effort in getting to know you, and this should be seen as encouraging to you. 2. When I decide to date someone, I will stop meeting other people. So you don't have to fear that I am double crossing you"
Of course, don't use my words, just reformulate/edit/delete as you see fit.