Answer: Your copycat coworker sounds both weird and annoying. But since you have to work with this pathetic person, you might as well view her imitation as a bizarre form of flattery.
You can’t stop her from choosing clothing and makeup similar to your own. And you can hardly tell her not to eat apples. However, you absolutely must prevent her from going through your belongings.
If you have any further evidence that she is looking in your purse or examining the contents of your desk, make it explicitly clear that this is not acceptable. If your desk has a lock, start using it.
Should she ever start doing really creepy things like calling you at home or showing up in unexpected places, you should immediately talk with your boss or human resources manager. Your unwelcome admirer probably isn’t a stalker, but you can’t be too careful.