Yes it does, but if. Left untreated there is no doubt that depression will come in some form or other. It's less likely that a person who is depressed and not bulimic will develop bulimia. Emotional, physical or sexual trauma/abuse very often leads to both bulimia and depression, not necessarily in that order.
Yes. Anyone can have bulimia, depressed or not. However, those with bulimia are much more likely to be depressed at the same time. Often antidepressants are used as part of a treatment plan for bulimia. If you are struggling with bulimia, see your doctor; effective treatment is available.
Yes. Bulimia is a way of numbing, distracting or expressing a variety of internal emotions and conflicts, including but not limited to depression. Bulimia can be a way of physically relieving anxiety, psychologically expressing conflicts about needs and wants, and other internal conflicts.