In answer to your additional questions, which are great by the way, I do think many girls try dieting on for size, and statistics suggest this is happening at younger and younger ages (80% of 10 year olds have worried about their appearance and tried/want to diet). However, I don't think its as easy to try an eating disorder on for size. In my experience, there is usually much more going on than just worry about appearance when someone develops an eating disorder. Think about it, most women worry about appearance a lot, yet eating disorders are still fairly rare, particularly anorexia. So, usually there are other issues and control of food/weight/body shape is something that's easier to focus on than those other issues.
About your daughter, depending on how long you've noticed her eating habits being unusual, you should talk to her about it - Alone, one on one (at the dinner table in front of the family will only make her feel attacked and put her on the defensive). If it hasn't been going on too long, you might monitor for awhile - maybe her eating habits will return to normal and she's just experimenting. If its been longer than a couple of weeks, find a time alone with her and express your concerns about her. Tell her you are worried about her, concerned that she may be trying to starve herself based on what you've seen, and that you worry about her developing an eating disorder. This is an ENTIRELY DIFFERENT APPROACH than trying to control food, although both are driven by the same motivations. Expressing concern and worry, however, will help her be less defensive, and show her how much you love her and care about her.
Don't expect much in this first exchange. She is likely to deny anything, and keep in mind that you may be wrong in your conclusions. Be willing to listen to what she has to say, letting her know your concerns all along. Then keep monitoring quietly. If she continues to appear to not be eating, is losing weight, becomes more interested in food (i.e. collecting recipes, cooking or buying rich foods for others but not eating them herself, talking about food all the time), becomes irritable and more isolated, or you see any signs of bingeing/purging (she goes to the bathroom after eating anything,etc) talk to her again, and this time you will likely need to tell her you are taking her for an evaluation. She will likely argue with you again, but at this point you have much more evidence and in a loving way are saying that you, as her mother, are going to do what you think best.
Now, THAT was long!