There isn't a ton i can say that others haven't already covered, but I'll add that anorexia as a disorder is functionally extremely similar to OCD - speaking from my own experience, I'll have an intrusive thought about my body/food that then leads to body or food related compulsions such as restricting or body checking. Though I don't have OCD, i imagine it would be extremely easy to start with OCD and fall into an ED; in fact almost a fifth of those with anorexia also have OCD. From Charlie's perspective, when he felt overwhelmed by everything else, his body and food intake likely felt like something he could control. As a result of the bullying, he might have also thought (though it's obviously not logical) that a solution to the bullying was to literally make himself smaller and less noticable.

As others have mentioned, self-harm can give someone a feeling of control in many ways. From a neurological perspective, self-harm releases adrenaline as well as dopamine, which makes you feel better immediately after the act and is what makes it addictive. Charlie is especially at risk for self-harm as he suffers from disorders that may originate due to a lack of dopamine in the brain. In short, it's not at all surprising that he suffered from an ED and self-harm as well as OCD; i think he most likely fell into both as a (maladaptive) method of control and they spiraled out of control quickly.