I actually don't think shes really a pedophile. It says on her info page that her personality is d itzy and clumsy. If she were to be a pedophile, she would probably have a seductive personality.

I think that the reason yandere-chan sees her as a rival, is because shes substituting for the school nurse that week, and because Senpai supposedly is going to be under the weather that week. She will only be "fond of Senpai" because of her being female. Senpai being either sick or injured would trigger her motherly nature. It's just a part of psychology that she would see Senpai as someone she needs to care for as if he were her own child. Especially if he happens to be her first patient that week. Therefore, if she gives Senpai a lot of caring attention, Yandere-chan would see her as a rival.