Twitter questions - I'm new user!?

[Tyjtynf]

Okay, so I made Twitter because I wanted to get it touch with this very minor celebrity, but was disappointed to learn that you can't send Direct Messages to people who are not following you. I think it's strange, 'cause I'm sure that there are people who would occassionally like to read the messages from their fans and there's no way I can do it. Writing a mention is uneffective, as you have very little space to actually write something and it's really not good way to introduce yourself, and randomly replyng to some of their posts is even more so. I had an idea to write a mention to the person and ask her to follow me, so that I can write her DM, but it's kinda stupid and not so possible. Also, how can I see when the person's online, so that I can write her something that she will reply to immedieately (if she wants to, of course).
There are lot of questions, so thanks in advance.