Why does Julia write the "I Love You" note to Winston and why is it so dangerous?
I believe that Julia writes that note to Winston because she senses in him a kindred soul. What I mean by this is that she sees him as someone else who hates the Party and what it stands for.
The note is so dangerous because people in that society are not supposed to love each other. Julia herself is part of the Junior Anti-Sex League, which is meant, in part, to keep people from forming romantic attachments. This is meant to keep the people from being attached to anything but the Party and Big Brother. So trying to become emotionally intimate with someone is really subversive, it would undermine the society if people did that.