Re: need advice asap
It sounds like you're an amazing boyfriend. Your girlfriend will be going through a mentally and emotionally really hard time at the moment, and the fact that you're sticking around for her will be appreciated even if she doesn't show it - I am so so grateful to my friends who stuck with me through everything and didn't desert me even when I didn't want to know them.
If she's going on pro anorexia websites then it sounds like she doesn't want to recover (right now at least), and unless she is on board with recovery then it's not something you can force.
Be there for her, support her, accept that she may have mad mood swings and not want to know you at times, but be hanging on your shoulder at others, but don't accept her illness. My mum was my biggest help when I was recovering, and though she didn't get mad at me and she accepted that she couldn't understand what was going on, she let me know that she was worried for me and that my way of life was going to destroy me in the end. Encourage her to spend time in the 'real' world and not online - where she can spend time with happy, healthy people and hopefully be encouraged that that is something to strive for.
Writing a note to her and encouraging her to write back is a great idea. It's likely that this isn't all about food, and that there are other issues there that are causing her to relapse (self esteem, perfectionism and control are relatively common ones, though also things like fear of abandonment, feeling that they don't deserve to live, and hundreds more).