P.S. The deadline is on wednesday, 10.11.2011 00:00 CET.
Thanks to anyone who helps, if I dont get help, thanks anyway.
You're almoost there. You've got some time left, so go in and work on the line segments yourself. You're not going to learn the tools and skills necessary to do this type of work if someone helps you cheat. We're doing you a favor by not helping you. This is close to a real world project because you've been given a deadline and it's up to you to get the job done. You will be proud of yourself for achieving what you thought was unachievable. Now get cracking!
Have to say I agree with John. You're in a class therefore you need to practise and learn, not have someone do it for you. Post a screenshot of where you're at and perhaps we can give some tips so that you can do a better job yourself.
Just a few words in addition to what John and Joe said (I am still with 10, so I could only open the file as PDF, and had to leave for quite a while):
The Direct Selection Tool and the Convert Anchor Point Tools may be your friends; the former may be used for adjusting handles, too, and (since you have Live Paint which allows sloppier path building) it allows Joining of open end Anchor Points.
Edit: I hope we shall not have the rest of the class here soon.
Put the image on a layer of its own. Lock it.
Put the drawing on its own layer. Set the drawing layer to Outline view. That way you can see crisp paths. Your strokes are at 4 pt and you won't achieve accuracy that way.