This post isn't breaking any sub rules that I'm aware of, but it doesn't really belong here. I don't know where to tell you to put it, though. You could maybe try r/loseit or r/1200isplenty? I don't know if it would really fit there, either. (Those are both weight loss/maintenance-related subs).

Should I be telling her to see a doctor or something?

That might not go over well, but it's clearly what she needs to do. Remind her that even if her habits were less severe, she would be wise to see a doctor just to make sure she's staying safe and healthy. She might be avoiding the doctor out of embarrassment, or it could be that she knows she's not eating properly.

Is this how anorexia happens?

I'm no expert on this, but I'm gonna say probably not. Plenty of people go on really restrictive plans just to lose weight. They know that they're being ridiculous with the way they're eating/exercising, but they don't really care.

Anorexia isn't behavioral, though. The behavior stems from the illness. An anorexic is deluded and believes that they are eating enough, and they have a skewed perception of their body, believing they are treating it properly by creating extreme caloric deficits. Anorexics need to treat the underlying mental illness before they can physically recover.

It doesn't sound like your roommate really thinks that she's eating properly, from what you described. She probably doesn't have body perception issues. She know's she's fat, and she's taking extreme measures to get not fat.

That said, I think she'd definitely do best if she got some therapy. Even if she doesn't have an eating disorder, she's doing really poorly after that break-up, and she needs to learn that taking things like weight-loss slowly is often much healthier.